Question

if one zero of p(x)= 2x^2-3x+p is 3, find the value of p and the other root.

Answer 1

Answer:

The value of p is -9

the other root is -3/2

Step-by-step explanation:

If one zero of p(x)= 2x^2-3x+p is 3, find the value of p and the other root.

Given:

$P(x)= 2x^2-3x+p$

since one zero is 3, P(3)=0

$\implies\:2(3)^2-3(3)+p=0$

$\implies\:2(9)-9+p=0$

$\implies\:9+p=0$

$\implies\:p=-9$

$P(x)= 2x^2-3x-9$

$= 2x^2-6x+3x-9$

$= 2x(x-3)+3(x-3)$

$=(2x+3)(x-3)$

$P(x)=0$

$\implies\:(2x+3)(x-3)=0$

$\implies\:x=-3/2,3$

The other root is -3/2