Question

$\text{If 2 is a zero of the polynomial of}p\left(z\right)=7z-a\text{and}(a+2)\text{is a zero of}\text{another polynomial}q\left(x\right)=a{x}^2+bx+c,\text{which of the following is true?}$

• A. $16a+c=0$
• B. $16b+c=0$
• C. $256a+16b+c=0$
• D. $a+b+c=0$

Answer 1

The correct option is C $256a+16b+c=0$

$\because \text{2 is a zero of polynomial}p\left(z\right),p\left(2\right)=0$
$\Rightarrow 7\left(2\right)-a=0$
$\Rightarrow 14-a=0$
$\Rightarrow a=14$

$\text{Given,}a+2=14+2=16\text{is a zero}\text{of the polynomial}q\left(x\right).$
$\Rightarrow$ $q\left(16\right)=0$
$\Rightarrow$ $q\left(16\right)=a\left({16}^2\right)+b\left(16\right)+c=0$
$\Rightarrow$ $256a+16b+c=0$