Question

7. Find the quadratic polynomial whose zeroes are -2 and -5.
Verify the relationship between zeroes and co-efficients of the
polynomial.​

Answer 1

GIVEN :

Zeroes of polynomial are -2 and -5

We know that,

Quadratic Polynomial :

p(x) = x² - (sum of zeroes)x + product of zeroes

Let the zeroes be α and β

α = -2 and β = -5

Sum of zeroes = (α + β) = (-2) + (-5) = -2 - 5 = -7

Product of zeroes = αβ = (-2)(-5) = 10

p(x) = x² - (α + β)x + αβ

p(x) = x² - (-7)x + (-10)

p(x) = x² + 7x - 10

Thus, polynomial = x² + 7x + 10

Relation between zeroes and coefficients :

From the above polynomial,

a = 1 ; b = 7 ; c = 10

Sum of zeroes = α + β = -b/a = -(7)/1 = -7

Product of zeroes = αβ = c/a = 10/1 = 10

Hence, Verified !!

Answer 2

Step-by-step explanation:

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