Question

If alpha beta are the two zeroes of the polynomial x^2-2x-8 then form a quadratic polynomial whose zeroes are 3alpha and 3beta

Answer 1

x^2 - 2x-8=0
x^2 - 4x+2x-8=0
x=4,-2
Therefore
Alpha =4,beta = - 2
3alpha=12,3 beta=-6
Sum of roots=6
Products of roots =-72
Equation=x^2 - (sum) x+(product)
Thus equation is
x^2 - 6x-72
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