Question

If one zero of the polynomial 2x^2+px+4=0 is 2,find the other zero & find the value of p

Answer 1

Answer:

p = -6  and other zero is 1.

Step-by-step explanation:

Given :

$\large \text{ p(x)=2x^2+px+4=0 and one zero is 2}$

putting x = 2 in p( x )

$\large p(x)=2x^2+px+4=0\\\\\\\large p(2)=2.(2)^2+2p+4=0\\\\\\\large p(2)=8+2p+4=0\\\\\\\large p(2)=12+2p=0\\\\\\\large p(2)=6+p=0\\\\\\\large p=-6$

Thus we get p = -6

Now put p = -6 in p ( x )

$\large p(x)=2x^2+px+4=0\\\\\\\large p(x)=2x^2-6x+4=0\\\\\\\large \text{By splitting mid term method we get}\\\\\\\large p(x)=2x^2-4x-2x+4=0\\\\\\\large p(x)=2x(x-2)-2(x-2)=0\\\\\\\large p(x)=(x-2)(2x-2)=0\\\\\\\large x-2=0 \ or \ 2x-2=0\\\\\\\large x=2 \ or \ x=1$

So one zero is 2 and other is 1.