Question

Find a quadratic polynomial the sum and product of whose zeros are - 1 and minus 20 respectively hence find the zero

Answer 1

${x - sx + p$
Where s is equal to sum of zeroes& p is equal to product of zeroes

Answer 2

Answer:

The two zeroes are 4 and -5

And the required quadratic equation is : x² + x - 20 = 0

Step-by-step explanation:

Let the two zeros of the quadratic polynomial be a and b

Then according to the given condition in the question, We get

a + b = -1 ......(1) , and

a·b = -20

$\implies a =\frac{-20}{b}$

Putting this value in equation (1)

$\frac{-20}{b}+b=-1\\\\\implies b^2+b-20=0\\\\\implies b = 4\:\:,\:\: or\:\:b=-5$

Putting these values in equation (1)

We get, a = -5 and a = 4

So, the two zeroes are 4 and -5

And the required quadratic equation is : x² + x - 20 = 0