Question

Find the zeros of the following quadratic polynomials :
$p\left(x\right)=x^2+4x-21$

Answer 1

In the given polynomial $x^2+4x-21$,

The first term is $x^2$ and its coefficient is $1$.

The middle term is $4x$ and its coefficient is $4$.

The last term is a constant term $-21$.

Multiply the coefficient of the first term by the constant $1\times -21=-21$.

We now find the factor of $-21$ whose sum equals the coefficient of the middle term, which is $4$ and then factorize the polynomial $x^2+4x-21$ and equate it to $0$ as shown below:

$x^2+4x-21=0\Rightarrow x^2+7x-3x-21=0\Rightarrow x(x+7)-3(x+7)=0\Rightarrow (x-3)(x+7)=0\Rightarrow (x-3)=0,(x+7)=0\Rightarrow x=3,x=-7$

Hence, the zeroes of the polynomial $x^2+4x-21$ are $-7,3$.