Find a quadratic polynomial whose zeroes are and 2
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7. Find the quadratic polynomial whose zeroes are -2 and -5.
Verify the relationship between zeroes and co-efficients of thepolynomial.
Answered by admin @
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 !!
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