Question

Find the quadratic polynomial sum and product of whose zeroes are -1 and -20 respectively. Also, find zeros of the polynomial so obtained.
If you answer fart iwill mark u as brainliset

Answer 1

Polynomials

Formula. If $\mathsf{p,\:q}$ be the zeroes of any quadratic polynomial, then it is found as follows,

$\quad\quad \mathsf{f(x)=x^{2}-(p+q)x+pq}$.

Solution.

Let $\mathsf{\alpha,\:\beta}$ be the zeroes of the given polynomial. Then

$\quad\quad\mathsf{\alpha+\beta=-1}$

$\quad\quad\mathsf{\alpha\beta=-20}$

Thus the required polynomial is

$\quad \mathsf{f(x)=x^{2}-(\alpha+\beta)x+\alpha\beta}$

$\Rightarrow \mathsf{f(x)=x^{2}-(-1)x+(-20)}$

$\Rightarrow \boxed{\color{red}{\mathsf{f(x)=x^{2}+x-20}}}$.

To find the zeroes of the polynomial.

The polynomial is

$\quad \mathsf{f(x)=x^{2}+x-20}$

$\Rightarrow \mathsf{f(x)=x^{2}+5x-4x-20}$

$\Rightarrow \mathsf{f(x)=x(x+5)-4(x+5)}$

$\Rightarrow \mathsf{f(x)=(x+5)(x-4)}$

$\Rightarrow \mathsf{x=-5,\:4}$

Hence the zeroes of the given polynomial are $\color{red}{\mathsf{(-5)}}$ and $\color{red}{\mathsf{4}}$.

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