Question

If the alfa and the beta are the zeroes of 2x2 - 5x + 7, then find the quadratic polynomial whose zeroes are 3l + 4B and 4l + 3B

Answer 1

i think instead of 7 it should be -7 then answer will be right

Answer 2

When roots are given, equation in quadratic form

x2−(α+β)x+αβ=0

Here roots are (2α+3β) and (3α+2β)

∴x2−(2α+3β+3α+2β)x+(2α+3β)(3α+2β)=0

x2−5(α+β)x+6α2+4αβ+4αβ+6β2=0

f(x)=2x2−5x+7

α+β=25, αβ=27

∴α2+β2=(α+β)2−2αβ

=425−7=4−3

x2−5(25)x+6(−43)+13×27