- 16 x 2 - 8 x + c = 0 In the given equation, c is a constant. The

Question

- 16 x 2 - 8 x + c = 0 In the given equation, c is a constant. The equation has exactly one solution. What is the value of c ?

Accepted Answer

The correct answer is - 1 . A quadratic equation in the form a x 2 + b x + c = 0 , where a , b , and c are constants, has exactly one solution when its discriminant, b 2 - 4 a c , is equal to 0 . In the given equation, - 16 x 2 - 8 x + c = 0 , a = - 16 and b = - 8 . Substituting - 16 for a and - 8 for b in b 2 - 4 a c yields - 8 2 - 4 - 16 c , or 64 + 64 c . Since the given equation has exactly one solution, 64 + 64 c = 0 . Subtracting 64 from both sides of this equation yields 64 c = - 64 . Dividing both sides of this equation by 64 yields c = - 1 . Therefore, the value of c is - 1 .

Question 16-x-2