Question

If a and b are the zeroes of 21y2-y-2 find a quadratic equation whose zeroes are 2a and 2b

Answer 1

α,β are the zeros of 21y²-y-2=0

then, α+β=-(-1/21)=1/21 and α×β=-2/21

i) now, 2α+2β=2(α+β)=2(1/21)=2/21 and

 2α×2β=4αβ=4×(-2/21)=-8/21

the equation having zeros 2α and 2β is:

x²-(sum of the zeros)x+product of the zeros=0

or, x²-(2/21)x+(-8/21)=0

or, x²-2x/21-8/21=0

or, 21x²-2x-8=0

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