Question

One root of px2

– 18x + 8 = 0 is eight times the other then p is

(A)0 (B) 3 (C) 1/3 (D) 4​

Answer 1

Step-by-step explanation:

Let one root be y. Then, other root is 8y.

Sum of roots is y+8y=9y.

So, 9y=18/p So, y=2/p ---- (1)

Product of the roots is 8(y)^2.

So,

$8 {y}^{2} = \frac{8}{p} \\ {y}^{2} = \frac{1}{p} \\ {( \frac{2}{p} )}^{2} = \frac{1}{p} \\ \frac{4}{ {p}^{2} } = \frac{1}{p} \\ {p}^{2} = 4p \\ p = 0 \: or \: p = 4$

So, p=0, 4.

Option D is the right answer.

Thank you