Question

find a quadratic polynomial,the sum and product of whose zeroes are -1 and -20 respectively.Hence find the zeroes

Answer 1

X2+X-20


I hope this might help u

Answer 2

Answer:

The required polynomial is $P(x)=x^2+x-20$. The zeroes of the polynomial are -5 and 4.

Step-by-step explanation:

If α and β are two zeroes of a polynomial then the polynomial is defined as

$P(x)=x^2-(\alpha +\beta)x+\alpha \beta$

It is given that the sum and product of zeroes are -1 and -20 respectively. So, the required polynomial is

$P(x)=x^2-(-1)x+(-20)$

$P(x)=x^2+x-20$

Therefore the required polynomial is $P(x)=x^2+x-20$.

Equate P(x)=0, to find the zeroes of the polynomial.

$x^2+x-20=0$

$x^2+5x-4x-20=0$

$x(x+5)-4(x+5)=0$

$(x+5)(x-4)=0$

$x+5=0\Rightarrow x=-5$

$x-4=0\Rightarrow x=4$

Therefore the zeroes of the polynomial are -5 and 4.