Question

If a polynomial $p\left(x\right)=x^2-ax+b$ has two zeroes 1 and 7, what is the value of $ab$?

• A. 8
• B. 56
• C. 42
• D. 7

Answer 1

The correct option is B 56

$\because$ 1 is a zero,
$p\left(1\right)=0$
$\Rightarrow$ $1^2-a+b=0$
$\Rightarrow$ $a-b=1$......eq (i)

Also,
$\because$ 7 is also a zero,
$p\left(7\right)=0$
$\Rightarrow$ $7^2-\left(7\right)a+b=0$
$\Rightarrow$ $7a-b=49$......eq (ii)

Subtracting (i) from (ii), we have
$7a-b-a+b=48$
$\Rightarrow$ $6a=48$
$\Rightarrow$ $a=8$

Substituting $a=8$ in eq (i), we have
$8-b=1$
$\Rightarrow$ $b=7$

$\therefore$ $ab=\left(8\right)\left(7\right)=56$