Determine the value of c if y=3x2+6x-c only has 1 x‒intercept. 

Prove algebraically.

in Algebra 1 Answers by Level 1 User (360 points)

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1 Answer

3x²+6x-c must have only one root, so 3(x²+2x-c/3) must contain a perfect square.

Therefore x²+2x-c/3 is a perfect square. This can be written x²+2x+1-1-c/3=(x+1)²-1-c/3.

And -1-c/3=0 so that the single root can be x=-1. Therefore c/3=-1, c=-3.

The quadratic becomes 3x²+6x+3=3(x+1)².
by Top Rated User (782k points)

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