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If alpha and beeta are zeroes …

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If alpha and beeta are zeroes Of the quadratic polynomial x2-6x+a, find the value of a, if 3 alpha+2 beeta=20

Posted by Chinnu S 5 years ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 11 months ago

Polynomial P(x) = x² - 6 x + a
Given  α and  β are the roots. To find a , if 3 α + 2 β = 20. ---(1)

From the quadratic expression:
α + β = 6 ---(2)
and α β = a --- (3)

Multiply equation (2) by 2 and subtract from (1) to get:
  α = 20 -12 = 8

Substitute this value in(2) to get:
β = 6-8 = -2

Substitute these in (3) to get: a = α β = -16.

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