solve a quadratic equation, showing all working out.

Question

solve the quadratic equation 3x^2-4x-2

give your answer to 3 significant figures

Answer 1

The equation would be:

3x²-4x-2=0, divide through by 3:

x²-4x/3-2/3=0,

x²-4x/3=2/3, complete the square:

x²-4x/3+4/9=2/3+4/9=10/9,

(x-2/3)²=10/9,

x-2/3=±√10/3,

x=2/3±√10/3, x=1.721 or -0.387 approx.

The same result can be obtained using the formula:

x=(4±√(16+24))/6=(4±√40)/6=(4±2√10)/6=(2±√10)/3.