Question

One of the zeroes of the polynomial is $2x^2+7x–4$ is

• A.
  $2$
• B.
  $\frac{1}{2}$
• C.
  $-\frac{1}{2}$
• D.
  $-2$

Answer 1

The correct option is B

$\frac{1}{2}$
Let $p\left(x\right)=2x^2+7x-4$
$=2x^2+8x–x–4$ [By splitting middle term]
$=2x(x+4)-1(x+4)$
$=(2x–1)(x+4)$
For zeroes of p(x), put p(x)=0.
$\therefore (2x-1)(x+4)=0$
$\Rightarrow 2x-1=0$ and $x+4=0$
$\Rightarrow x=\frac{1}{2}$ and $x=-4$
Hence, one of the zeroes of the polynomial p(x) is $\frac{1}{2}$.