9. If a and B the zeros of the polynomial f(x) = x^2 + px +q, form a polynomial whose
zeros are (a + b)^2 and (a - b)^2
Answers
Answered by
1
Answer:
f(x)=x
2
+px+q
Roots are α and β
α+β=−p
αβ=q
(α+β)
2
=p
2
(α−β)
2
=(α+β)
2
−4αβ
p
2
−4q
New Roots are (α+β)
2
and (α−β)
2
Sum=(α+β)
2
+ (α−β)
2
=p
2
+p
2
−4q
=2(p
2
−2q)
Product=(α+β)
2
(α−β)
2
=p
2
(p
2
−4q)
∴f(x)=K(x
2
−2(p
2
−2q)x+p
2
(p
2
−4q
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