Question

If 2 is a zero of the polynomial $p\left(x\right)=x^3-a{x}^2+bx+c,$ then which of the following equations is true?

• A. $-2a+4b+c+8=0$
• B. $-4a+2b+c+8=0$
• C. $4a+4b+c+8=0$
• D. $-4a-2b+c-8=0$

Answer 1

The correct option is B $-4a+2b+c+8=0$

Since 2 is a zero of the polynomial p(x), p(2) = 0.
$\Rightarrow 2^3-a\left(2^2\right)+b\left(2\right)+c=0$
$\Rightarrow 8-4a+2b+c=0$
$\Rightarrow -4a+2b+c+8=0$