Question

Verify whether the following values indicated against them are zeroes of the polynomial.
$\left(i\right)p\left(x\right)=5x-\pi ,x=\frac{4}{5}$
$\left(ii\right)p\left(x\right)=x^2-1,x=1,-1$ [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1.5 Marks each

$\left(i\right)p\left(x\right)=5x-\pi ,x=\frac{4}{5}$

$p\left(\frac{4}{5}\right)=5\left(\frac{4}{5}\right)-\pi =4-\pi$

$p\left(\frac{4}{5}\right)\ne 0$

$\frac{4}{5}$ is not the zero of the polynomial $p\left(x\right)=5x-\pi$.


$\left(ii\right)p\left(x\right)=x^2-1,x=1,-1$

$p\left(1\right)=1^2-1=1-1=0$

$p(-1)={(-1)}^2-1=1-1=0$

Both p(1) and p(−1) are equal to 0. It means that 1 and -1 are zeroes of the polynomial $p\left(x\right)=x^2-1$.