Question

answer this question ​

Answer 1

Step-by-step explanation:

As we have given,

sum of the zeros of the quadratic polynomial is -1 and the product of zeros of quadrilateral polynomial is -20

let us consider the roots are, α andβ

( α + β ) = -1

(α.β) = -20 __________(1)

we know the formula to making a quadratic equation,[x² -(α+β)x+(α.β)]

x² - (-1)x + (-20)

x² + x - 20

so the required quadratic equation is x² + x - 20

(α + β ) = -1

α = -1 - β

put the value of α an equation (1)

(α.β) = -20

((-1-β).β) = -20

-β - β² = -20

-β² -β + 20 = 0

getting (-1) on both the sides

β² + β - 20 = 0

β² + 5β - 4β - 20 = 0

β(β + 5) -4 (β + 5)= 0

(β - 4) (β + 5) = 0

β = 4 or β = -5

therefor the roots of the given quadratic polynomial are ,

if β = 4 then α = -1 - (4) = -5

α = -5

if β = -5 then α = -1 - (-5) = -1 + 5 = 4

α = 4