Find the quadratic polynomial, sum of whose zeroes is 0 and their product is $-1$. Hence, find the zeroes of the polynomial.

Home » Find the quadratic polynomial, sum of whose zeroes is 0 and their product is . Hence, find the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is $-1$ . Hence, find the zeroes of the polynomial.

Find the quadratic polynomial, sum of whose zeroes is 0 and their product is $-1$ . Hence, find the zeroes of the polynomial.

Let $\alpha$ and $\beta$ be the zeroes of the required polynomial $f(x)$ .

Then $(\alpha+\beta)=0$ and $\alpha \beta=-1$

$\therefore f(x)=x^{2}-(\alpha+\beta) \mathrm{x}+\alpha \beta$

$\Rightarrow f(x)=x^{2}-0 x+(-1)$

$\Rightarrow \mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-1$

Hence, required polynomial $f(x)=x^{2}-1$ .

$\therefore f(x)=0 \Rightarrow x^{2}-1=0$

$\begin{aligned} &\Rightarrow(x+1)(x-1)=0 \\ &\Rightarrow(x+1)=0 \text { or }(x-1)=0 \\ &\Rightarrow x=-1 \text { or } x=1 \end{aligned}$

So, the zeroes of $\mathrm{f}(\mathrm{x})$ are $-1$ and 1 .

i

Sign up now and study all subjects for free