if α and β are the zeroes of the polynomial x^2-4x+3 then find the quadratic polynomial whose roots are 3α and 3β.
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Best answer will be marked as brainliest....
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For steps see the above attached pic.
=x^2-3x-x+3
=x(x-3)-1(x-3)
=(x-3)(x-1)
so x = 3 and x =1
so,alpha = 3 and beta = 1
so,roots of the required polynomial are 9 and 3
now, let the polynomial be ax^2 + bx + c
so, alpha + beta = -b/a
9+3 = -b/a
12 = -b/a
and, alpha × beta = c/a
9×3 = c/a
27 = c/a
so, a = 1 ,b = -12 and c =27
so,the polynomial is x^2-12x+27