If alpha and beta are roots of equation ax^2 +bx +c=0, Then the roots of equation ax^2-bx(x-1)+c(x-1)^2 are - Maths - Complex Numbers and Quadratic Equations

Question

If alpha and beta are roots of equation ax^2 +bx +c=0, Then the
roots of equation ax^2-bx(x-1)+c(x-1)^2 are?

Anuradha Sharma · Accepted Answer

Hi, from the first equation, ax2+bx+c=0 α+β= -baand αβ= caax2-bx2+bx+cx2+c-2cx= 0 x2a-b+c+xb-2c+c=0 its roots are x = 2c-b±b2+4c2-4bc-4ac+4bc-4c22a-b+c= 2c-b±b2-4ac2a-b+cNow divide by a = 2ca-ba±ba2-4ca21-ba+ca= 2αβ+α+β±α+β2-4αβ21+α+β+αβ=2αβ+α+β±α-β21+α+β+αβ= 2αβ+α+β+α-β21+α+β+αβ or 2αβ+α+β-α-β21+α+β+αβSimplify this to get the answer
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If alpha and beta are roots of equation ax^2 +bx +c=0, Then the roots of equation ax^2-bx(x-1)+c(x-1)^2 are?