Question

One of the roots of the quadratic equation x^2+16x+q=0 is −1. Find q.

Answer 1

The value of q is 15.

Explanation:

Given equation,

`x^2 + 16x + q =0`

We know that roots of an equation satisfies the equation,

i.e. if x = -1 is one of the roots of the equation,

Then,

`(-1)^2 + 16(-1) + q =0`

`1 - 16 + q=0`

`-15 + q=0`

`\implies q = 15`

Hence, the value of q is 15.

Answer 2

q = 15

Explanation:

The sum of the roots is the opposite of the x-coefficient, so the other root is ...

r - 1 = -16

r = -15 . . . . . the other root of the equation

The product of the roots is q, so ...

q = (-1)(-15) = 15