Question

Find the zeroes of the following polynomials by factorisation method :
$4x^2-3x-1$.

• A. $-\frac{1}{4}$
• B. $1$
• C. $\frac{1}{4}$
• D. $-1$

Answer 1

Answer: (A), (B)

The correct options are
A $-\frac{1}{4}$
B $1$

Let $f\left(x\right)=4x^2-3x-1$.
Comparing it with the standard quadratic polynomial $a{x}^2+bx+c$, we get,
$a=4$, $b=-3$, $c=-1$.
Now, $4x^2-3x-1$
$=4x^2-4x+x-1$
$=4x(x-1)+1(x-1)$
$=(x-1)(4x+1)$.
The zeros of $f\left(x\right)$ are given by $f\left(x\right)=0$.
$=>(x-1)(4x+1)=0$
$=>(x-1)=0$ or $(4x+1)=0$
$=>x=1$ or $x=\frac{-1}{4}$.
Hence the zeros of the given quadratic polynomial are $1$, $\frac{-1}{4}$.

Hence, options $A$ and $B$ are correct.