2 x 2 - 8 x - 7 = 0 One solution to the given equation can be written as

Question

2 x 2 - 8 x - 7 = 0 One solution to the given equation can be written as 8 - k 4 , where k is a constant. What is the value of k ?

Accepted Answer

The correct answer is 120 . The solutions to a quadratic equation of the form a x 2 + b x + c = 0 can be calculated using the quadratic formula and are given by x = - b &plusmn; b 2 - 4 a c 2 a . The given equation is in the form a x 2 + b x + c = 0 , where a = 2 , b = - 8 , and c = - 7 . It follows that the solutions to the given equation are x = 8 &plusmn; - 8 2 - 4 2 - 7 2 2 , which is equivalent to x = 8 &plusmn; 64 + 56 4 , or x = 8 &plusmn; 120 4 . It's given that one solution to the equation 2 x 2 - 8 x - 7 = 0 can be written as 8 - k 4 . The solution 8 - 120 4 is in this form. Therefore, the value of k is 120 .

Question 2-x-2-