Question

find the zeros of :
x^{2} +x-30

Answer 1

Answer:

The zeros of the quadratic polynomial is -5 and 6.

Consider the provided polynomial.

x^2-x-30x

2

−x−30

Let p(x)=x^2-x-30p(x)=x

2

−x−30

Substitute p(x)=0 and split the middle term.

x^2-6x+5x-30=0x

2

−6x+5x−30=0

x(x-6)+5(x-6)=0x(x−6)+5(x−6)=0

(x+5)(x-6)=0(x+5)(x−6)=0

\begin{gathered}x+5=0\ or\ x-6=0\\x=-5\ or\ x=6\end{gathered}

x+5=0 or x−6=0

x=−5 or x=6

Thus, the zeros of the quadratic polynomial is -5 and 6.

Verify:

\text{Sum of zeros}=-\frac{\text{Coefficient of }x}{\text{Coefficient of }x^2}Sum of zeros=−

Coefficient of x

2

Coefficient of x

\begin{gathered}-5+6=-\frac{-1}{1}\\1=1\end{gathered}

−5+6=−

1

−1

1=1

Which is true.

\text{Product of zeros}=\frac{\text{Constant term}}{\text{Coefficient of }x^2}Product of zeros=

Coefficient of x

2

Constant term

\begin{gathered}-5\times6=\frac{-30}{1}\\-30=-30\end{gathered}

−5×6=

1

−30

−30=−30

Which is true.

#Learn more

Find the zero of the quadratic equations

Answer 2

$\huge \tt \blue {Answer}$

${x}^{2} + x - 30$

${x}^{2} + 6x - 5x - 30$

$x(x + 6) - 5(x + 6)$

$(x - 5)(x + 6)$

$\mathsf \red{The \: zeroes \: of \: the \: polynomial \: are \: - }$

$\red{(x - 5)(x + 6)}$