Question

If x = `1/2` and x = –2 are the roots of 2x² + px + q = 0, find the values of p and q.

Answer 1

Given:

2x² + px + q = 0

`x = 1/2` and x = −2

Using relations between roots and coefficients

For ax² + bx + c = 0:

Sum of roots = `-b/a`

Product of roots = `c/a`

Here, a = 2, b = p, c = q.

Sum of the roots

`1/2 + (-2)`

`= 1/2 -2`

`=-3/2`

`-p/2 = -3/2`

p = 3

Product of the roots

`1/2xx(-2) = -1`

`q/2 = -1`

q = −2

p = 3 and q = −2​