If ∝, are zeroes of the polynomial 2x2-5x+7, then find a quadratic
polynomial whose zeroes are 3∝+4 and 4∝+3.
Answers
Refer to the attachment and please mark brainliest
Answer:
Step-by-step explanation:
α² + β² can be written as (α + β)² - 2αβ
p(x) = 2x² - 5x + 7
a = 2 , b = - 5 , c = 7
α and β are the zeros of p(x)
we know that ,
sum of zeros = α + β
= -b/a
= 5/2
product of zeros = c/a
= 7/2
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3α + 4β and 4α + 3β are zeros of a polynomial.
sum of zeros = 3α + 4β + 4α + 3β
= 7α + 7β
= 7 x 5/2
= 35/2
product of zeros = (3α + 4β) (4α + 3β)
= 3α(4α + 3β) + 4β(4α+3β)
= 12α^2 + 9αβ + 16αβ + 12β^2
= 12α^2 + 25αβ + 12β^2
= 12(α^2 + β^2) + 25αβ
= 12[(α+β)^2-2αβ] + 25αβ
= 12[(5/2)^2 -2 x 7/2] + 25 x 7/2
= 12 x 25/4 -7 + 175/2
= 12 x -3/4 + 175/2
= -18/2 + 175/2
= 157/2