Question

find the quadratic polynomial the sum and product of whose zeros are - 1 and minus 20 respectively also find the zeros of the polynomial so obtained​

Answer 1

Answer:

quadratic equation is x^2+x-20=0

Answer 2

The quadratic equation with the sum and product of zeroes of the polynomial as -1 and -20 is $x^{2} + x - 20 = 0$ and the zeros of the polynomial are 4 and -5 .

• Given :

Sum of zeros of quadratic polynomial = -1

Product of zeros of polynomial = -20

• The general equation for a quadratic polynomial is $x^{2} - (Sum \ of \ zeroes)x + (Product \ of \ zeroes)$ = 0
• Now, the quadratic equation becomes ,

$x^{2} + x - 20$ = 0

• Now we find the zeros of the polynomial,
• The zeros of the polynomial are the roots of the polynomial .

$x^{2} + x - 20 = 0$

$x = \frac{-b+\sqrt{b^2-4ac}}{2a}$ or $x = \frac{-b-\sqrt{b^2-4ac}}{2a}$ , where a = 1 , b = 1 and c = -20

$x = \frac{-1+\sqrt{81}}{2}$ or $x = \frac{-1-\sqrt{81}}{2}$

$x = \frac{-1+9}{2}$ or $x = \frac{-1-9}{2}$

x = 4 and x = -5

• Therefore, the roots of the quadratic polynomial are 4 and -5 .