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If alpha and beta are the …

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If alpha and beta are the zeroes of p(x)=x2-3x-2 find the quadratic polynomial whose zeroes are - 2alpha 2beta

Posted by Vanshika Sharma 1 year, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Taniya . 1 year, 7 months ago

Given that α & β are zero of polynomial f(x)=x2−3x−2 therefore α+β=3 αβ=−2 Now, the zero of the required quadratic polynomial are, 2α+β1 & 2β+α1 Sum of the roots- 2α+β1+2β+α1=(2α+β)(2β+α)2β+α+2α+β=4αβ+2α2+2β2+αβ3(α+β) =4×(−2)+2[(α+β)2−2αβ]+(−2)3×3 =−10+2[9+2×2]9 =−10+269 =169 Products of roots:- 2α+β1×2β+α1=4αβ+2[(α+β)2−2αβ]+αβ1=161 Now Req eq. x2−(sum of roots)x+ Product of roots=0 =x2−169x+161=0 =16x2−9x+16=0.

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