Question

2. If a and B are the zeros of the quadratic polynomial f (x)=ax2+bx+c
(i)
a-B
${ax}^{2} + bx + c$
​

Answer 1

Step-by-step explanation:

Sum of the roots of the given equation =α+β=a−b    ...(1)

Product of the roots of the given equation =αβ=−ac    ....(2)

βα2+αβ2 =αβα3+β3=αβ(α+β)(α2−αβ+β2)=αβ(α+β)((α+β)2−2αβ−αβ)=αβ(α+β)((α+β)2−3αβ)    ....(3)

Substituting (1),(2) in (3), we get

βα2+αβ2=−c/a(−b/a)((−b/a)2−3(−c/a))=cb[a2

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