Question

5. If one zero of the polynomial q(x) = x2 + px + 8 is double the other, then find the value of p and hence both zeroes of q(x).​

Answer 1

Step-by-step explanation:

Given polynomial,

q(x) = x² + px + 8

Let one zero be 'x'

then the other zero is 2x.

We know,

Product of zeroes = constant/x² coefficient

(x) (2x) = 8

2x² = 8

x² = 8/2

x² = 4

x = √4

x = ±2

If x = +2,

Sum of zeroes = –(x coefficient)/x² coefficient

x + 2x = –p

3x = –p

3(2) = –p

6 = –p

p = –6

One zero = 2

Other zero = 2(2) = 4

If x = –2,

Sum of zeroes = –(x coefficient)/x² coefficient

x + 2x = –p

3x = –p

3(–2) = –p

–6 = –p

p = 6

One zero = –2

Other zero = 2(–2) = –4