1.

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

Answer»

Answer:

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p = -6  and other zero is 1.

Step-by-step explanation:

Given :

\large \text{$p(x)=2x^<klux>2</klux>+px+4=0$ and <klux>ONE</klux> zero is 2}

putting x = 2 in p( x )

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

THUS we get p = -6

Now put p = -6 in p ( x )

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

So one zero is 2 and other is 1.


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