Question

If 'p' is a root of the quadratic equation x² – (p + q) x + k = 0, then the value of 'k' is ______.

Options

• p

• q

• p + q

• pq

Answer 1

If 'p' is a root of the quadratic equation x² – (p + q) x + k = 0, then the value of 'k' is pq.

Explanation:

Let the roots of given quadratic equation be α and β.

On comparing equation x² – (p + q) x + k = 0

with ax² + bx + c = 0, we have

a = 1, b = –(p + q), c = k

We know that

`\implies` α + β = `(-b)/a`

Put the value a and b

`\implies` α + β = `(p + q)/1`

`\implies` α + β = p + q  ...(1)

Given α = p

Put the value of α in equation (1),

`\implies` p + β = p + q

`\implies` β = q

But we know that

α.β = `c/a`

Put the values

p.q. = `k/1`

Then, k = pq.