Question

If x = 2 and x = 1 are the zeroes of the quadratic polynomial $a{x}^2-3x+b,\text{then find the value of a - b}$.

• A. \N
• B. 1
• C. - 1
• D. 2

Answer 1

The correct option is C - 1

Let $f\left(x\right)=a{x}^2-3x+b.$
Since x = 2 is a zero of f(x), f(2) = 0.
$\Rightarrow 4a-6+b=\mathrm{0.......}\left(i\right)$

Also, since x = 1 is a zero f(x), f(1) = 0,
$\Rightarrow a-3+b=\mathrm{0.......}\left(ii\right)$

$\left(i\right)-\left(ii\right)\Rightarrow 3a=3$
$\Rightarrow a=1$
Thus, (ii) $\Rightarrow b=2$

Hence, (a-b) = 1 - 2 = - 1.