if alpha and bita are the zeroes of quadratic polynomial x2 - 2x +3 . find a polynomial whoes roots are . a alpha +2, bita +2
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Answer:
We Know that sum of zeroes = -b/a
and product= c/a
therefore, alpha + beta= -(-2/1) = 2
and alpha*beta= 3/1 = 3
now taking alpha +2 and beta +2
sum = alpha + 2 + beta + 2
= alpha + beta + 4
= 2 + 4 alpha + beta = 2
sum = 6
Product = (alpha + 2) (beta +2)
= alpha*beta + 2 alpha + 2 beta + 4 taking 2 as common
= 3 + 2 (alpha + beta) + 4 alpha*beta = 3
= 3 + 2 (2) + 4 alpha + beta = 2
=3 + 4 + 4
product =11
now if we have sum and product of zeroes the formula of polynomial is
x^2 - sum of zeroes + product of zeroes
= x^2 - 6 + 11 Ans
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