Question

Write the quadratic polynomial whose zeroes are $2,-4$.

Answer 1

Determine the quadratic polynomial.

Quadratic equations or quadratic polynomials are second-degree algebraic expressions and are of the form $a{x}^2+bx+c=0$.

The standard form of a quadratic polynomial with roots $m$ and $n$ is $x^2–(m+n)x+mn=0$.

Given roots are $2,-4$

$$\begin{gathered} m=2 \\ n=-4 \end{gathered}$$

Calculate the sum of the roots:

$$\begin{gathered} m+n=2+(-4) \\ \Rightarrow =-2 \end{gathered}$$

Calculate the product of the roots:

$$\begin{gathered} m\times n=2\times (-4) \\ \Rightarrow =-8 \end{gathered}$$

Putting the sum and product root value into the standard form of a quadratic polynomial:

$$\begin{gathered} x^2–(m+n)x+mn=0 \\ \Rightarrow x^2–(-2)x+(-8)=0 \\ \Rightarrow x^2+2x-8=0 \end{gathered}$$

Hence, the quadratic polynomial is $x^2+2x–8=0$.