Question

Find the zeros of the following quadratic polynomial:
$p\left(x\right)=4x^2+9x+5$

Answer 1

In the given polynomial $4x^2+9x+5$,

The first term is $4x^2$ and its coefficient is $4$.

The middle term is $9x$ and its coefficient is $9$.

The last term is a constant term $5$.

Multiply the coefficient of the first term by the constant $4\times 5=20$.

We now find the factor of $20$ whose sum equals the coefficient of the middle term, which is $9$ and then factorize the polynomial $4x^2+9x+5$and equate it to $0$ as shown below:

$4x^2+9x+5=0\Rightarrow 4x^2+4x+5x+5=0\Rightarrow 4x(x+1)+5(x+1)=0\Rightarrow (x+1)(4x+5)=0\Rightarrow (x+1)=0,(4x+5)=0\Rightarrow x=-1,4x=-5\Rightarrow x=-1,x=-\frac{5}{4}$

Hence, the zeroes of the polynomial $4x^2+9x+5$ are $-1,-\frac{5}{4}$.