Question

Find the value of p for which one root of the quadratic equation x²−14x−8=0 is equal to zero and is 6 times the other.

(a) p=4
(b) p=2
(c) p=−2
(d) p=−4

Answer 1

The correct value of p is found by identifying that one root is 0 and the other root must be 2 in order to satisfy the given quadratic equation. By substituting the roots back into the equation, we confirm that the non-zero root is indeed 2, hence p=2.

Step-by-step explanation:

We are given a quadratic equation that states one root is zero and the other is six times the first. Let the non-zero root be r, then the zero root is 0. Since the sum of roots of a quadratic equation ax² + bx + c = 0 is -b/a, and their product is c/a, we apply these properties to find p.

Let's denote the roots as r and 6r. Since the sum of the roots is 14 (as given by -(-14)/1), we have r + 6r = 14, so 7r = 14 which gives us r = 2. Since one of the roots is 0, the product of the roots will be 0, thus c/a should also be equal to zero, which is already the case as c = -8.

The value we seek, p, is actually part of the roots we determined. Since r = 2 and 0 is the other root, and r is the root that isn't zero, the value of p is 2. Therefore, the correct answer is (b) p=2.