Question

if -2 is a zero of a polynomial P(X) =ax³-x²+x+4 ,then find the value of "a"

Answer 1

Hi there !

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Given :

-2 is a zero of a polynomial p(x) = ax³ - x² + 4.

Solution :

P(x) = ax³ - x² + 4

Now,

On putting the value of x = -2 ,

$\mathsf{ax {}^{3} - x {}^{2} + x + 4 = 0 } \\ \\ \mathsf{ \implies a( - 2) {}^{3} - ( - 2) {}^{2} + ( - 2) + 4 = 0} \\ \\ \mathsf{ \implies - 8a - 4 - 2 + 4 = 0} \\ \\ \mathsf{ \implies - 8a - 2 = 0} \\ \\ \mathsf{ \implies - 8a = 2} \\ \\ \mathsf{ \implies a = - \frac{2}{8} } \\ \\ \mathsf{ \implies a = - \frac{1}{4} }$

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Thanks for the question !

Answer 2

$\mathbb{ \tiny{ \fcolorbox{green}{pink}{QUESTION:-:-}}}$

if -2 is a zero of a polynomial P(X) =ax³-x²+x+4 ,then find the value of "a".

$\mathbb{ \tiny{ \fcolorbox{green}{pink}{METHOD\: OF \: Solution:-:-}}}$

We Have Equation:-

               ax³-x²+x+4

One Zeros of Polynomial:- (-2)

To Find the value of Another Zeroes which means find the exact value of a;

Considering On Question Value!

Substitute the value of " X" in Given Polynomial;

  f(x)=>     ax³-x²+x+4

  f(-2)=>  a(-2)²-(-2)² +(-2)+4 =0

   f(-2)=> -8a-4-2+4= 0

    f(-2)=> -8a-4-2+4=0

   f(-2)=> -8a -2=0

  f(-2)=>  -8a-2=0

  f(-2)=> -8a-2=0

 f(-2)=>  -4a=2

•

• • Conclusion:- a=-1/4

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$\mathbb{ \huge{ \fcolorbox{green}{pink}{THANK \: YOU:-}}}$