72,125 questions

69,637 answers


46,764 users

MathHomeworkAnswers.org is a free math help site for student, teachers and math enthusiasts. Ask and answer math questions in algebra I, algebra II, geometry, trigonometry, calculus, statistics, word problems and more. Register for free and earn points for questions, answers and posts. Math help is always 100% free.

Note: This site is intended to help students and non-students understand and practice math. we do not condone cheating. Users attempting to abuse the system will be permanently blocked from further use.

Most popular tags

algebra problems solving equations word problems calculating percentages geometry problems calculus problems fraction problems trigonometry problems rounding numbers simplifying expressions solve for x math problem order of operations pre algebra problems evaluate the expression algebra slope intercept form factoring probability please answer this queastion as soon as possible. thank you :) please help me to answer this step by step. polynomials statistics problems plz. give this answer as soon as possible solving inequalities how to find y intercept algebra 2 problems logarithmic equations equation of a line solving systems of equations by substitution help sequences and series word problem dividing fractions greatest common factor graphing linear equations square roots geometric shapes substitution method long division 6th grade math least common multiple factoring polynomials solving systems of equations http: mathhomeworkanswers.org ask# solving equations with fractions standard form of an equation function of x ratio and proportion least to greatest dividing decimals proving trigonometric identities algebra problem trig identity solving equations with variables on both sides help me!! ( precalculus problems solving systems of equations by elimination help me slope of a line through 2 points domain of a function college algebra algebraic expressions trinomial factoring distributive property i need help with this factors of a number solving quadratic equations perimeter of a rectangle slope of a line division fraction word problems 8th grade math exponents limit of a function differentiation greater than or less than equivalent fractions differential equation how to find x intercept elimination method algebra 1 hw help asap geometry 10th grade simplifying fractions area of a triangle inverse function . 7th grade math geometry area of a circle integral simplify place value parallel lines standard deviation solving triangles fractions solving linear equations width of a rectangle circumference of a circle percentages systems of equations containing three variables mixed numbers to improper fractions scientific notation problems number of sides of a polygon zeros of a function algebra word problems lowest common denominator prime factorization solving systems of equations by graphing diameter of a circle length of a rectangle story problems area of a rectangle mathematical proofs quadratic functions dividing polynomials derivative of a function 5th grade math vertex of a parabola calculus homework converting fractions to decimals evaluating functions algebra 1 integers equation finding the nth term range of a function combining like terms ordered pairs calculators greatest to least perpendicular lines least common denominator unit conversion algebra 2 complex numbers solve for y radius of a circle ) solving radical equations slope area word problems functions what is the answers? calculus problem because i don't understand 4th grade math calculate distance between two points multiplying fractions common denominator statistics ratios set builder notation simplifying radicals binomial expansion percents help me please and show how to work it out math homework round to the nearest tenth geometry word problems midpoint of a line absolute value significant figures product of two consecutive numbers equation of a tangent line radicals #math show work () median solve show every step to solve this problem adding fractions please answer this question as soon as possible. thank you :) divisibility rules graphing functions graphing math pre-algebra problems roots of polynomials factor by grouping 1 - improper fractions to mixed numbers percentage place values number patterns ? subtracting fractions (explain this to me) volume of a cylinder decimals rational irrational numbers how to complete the square simultaneous equations numbers derivatives expanded forms solving equations with variables maths http: mathhomeworkanswers.org ask?cat=# please help = multiplying polynomials sets http: mathhomeworkanswers.org ask# need help solving quadratic equations by completing the square implicit differentiation integration divide mixed numbers surface area of a prism average rate of change algebra1 pemdas angles age problem rounding decimals comparing decimals solving trigonometric equations surface area of a cube logarithms trigonometry #help perimeter of a triangle 9th grade math matrices dividing geometry problem rounding to the nearest cent reducing frations to lowest terms arithmetic sequences factor how do you solve this problem in distributive property compound interest simplifying trigonometric equation using identities direct variation chemistry none mean lcm answer solve algebra equation probability of an event 5th grade math problems

Prove the quadratic equation

I need to understand the proof of the quadratic equation. I know that it can be done using a completing the square method.  Is it possible to do this quadratic equation proof without completing the square?
asked Apr 8, 2011 in Algebra 1 Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

A quadratic equation in the standard form is given by

ax 2 + bx + c = 0

where a, b and c are constants with a not equal to zero.
...Solve the above equation to find the quadratic fomulas

ax 2 + bx + c = 0

Divide all terms by a
x 2 + (b / a) x + c / a = 0

Subtract c / a from both sides
x 2 + (b / a) x + c / a - c / a = - c / a

and simplify
x 2 + (b / a) x = - c / a

Add (b / 2a) 2 to both sides
x 2 + (b / a) x + (b / 2a) 2 = - c / a + (b / 2a) 2

to complete the square
[ x + (b / 2a) ] 2 = - c / a + (b / 2a) 2

Group the two terms on the right side of the equation
[ x + (b / 2a) ] 2 = [ b 2 - 4a c ] / ( 4a2 )

Solve by taking the square root
x + (b / 2a) = ± sqrt { [ b 2 - 4a c ] / ( 4a2 ) }

Solve for x to obtain two solutions
x = - b / 2a ± sqrt { [ b 2 - 4a c ] / ( 4a2 ) }

The term sqrt { [ b 2 - 4a c ] / ( 4a2 ) } may be written
sqrt { [ b 2 - 4a c ] / ( 4a2 ) } = sqrt(b 2 - 4a c) / 2 | a |

Since 2 | a | = 2a when a > 0 and 2 | a | = -2a when a < 0, the two solutions to the quadratic equation may be written
x = [ -b + sqrt( b 2 - 4a c ) ] / 2 a

x = [ -b - sqrt( b 2 - 4a c ) ] / 2 a

The term b 2 - 4a c which is under the square root in both solutions is called the discriminant of the quadratic equation. It can be used to determine the number and nature of the solutions of the quadratic equation. 3 cases are possible

case 1: If b 2 - 4a c > 0 , the equation has 2 solutions.

case 2: If b 2 - 4a c = 0 , the equation has one solutions of mutliplicity 2.

case 3: If b 2 - 4a c < 0 , the equation has 2 imaginary solutions.

answered Apr 8, 2011 by mshelton Level 4 User (9,310 points)
Your c/a value is the product of the roots
Your -b/a value is the sum of your roots

Related questions

1 answer 23 views
23 views asked Aug 27 in Other Math Topics by jeshlin (160 points)
1 answer 28 views
28 views asked Jun 1 in Other Math Topics by Raj kishore
2 answers 42 views
42 views asked Oct 27, 2013 in Other Math Topics by mathematical proof
0 answers 29 views
29 views asked Oct 21, 2013 in Other Math Topics by anonymous
0 answers 33 views
33 views asked Aug 15, 2013 in Other Math Topics by Shenbagavalli.N
0 answers 26 views
26 views asked Jul 2, 2013 in Word Problem Answers by anonymous