Question

If p and q are the roots of the equation x² – px + q = 0, then ______.

Options

• p = 1, q = –2

• p = 1, q = 0

• p = –2, q = 0

• p = –2, q = 1

Answer 1

If p and q are the roots of the equation x² – px + q = 0, then p = 1, q = –2.

Explanation:

Given that p and q be the roots of the equation x² − px + q = 0

Then find the value of p and q.

Here, a = 1, b = –p and, c = q

p and q be the roots of the given equation

Therefore, sum of the roots

`p + q = (-b)/a`

= `(-p)/1`

= –p

q = –p – p

= –2p       ...(i)

Product of the roots

`p xx q = q/1`

As we know that `p = q/q`

= 1

Putting the value pf p = 1 in equation (i)

q = −2 × 1

= –2

Therefore, the value of p = 1; q = –2