SATHEE: Sequences and Series 3 Question 8

Sequences and Series 3 Question 8

8. Let $f (x) = a x^{2} + b x + c, a \neq 0$ and $Δ = b^{2} - 4 a c$ . If $α + β$ , $α^{2} + β^{2}$ and $α^{3} + β^{3}$ are in GP, then

(a) $Δ \neq 0$

(b) $b Δ = 0$

(d) $b c \neq 0$

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Answer:

Correct Answer: 8. (c)

Solution:

Since, $(α + β), (α^{2} + β^{2}), (α^{3} + β^{3})$ are in GP.

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Sequences and Series 3 Question 8

8. Let f(x)=ax2+bx+c,a≠0 and Δ=b2−4ac. If α+β, α2+β2 and α3+β3 are in GP, then

Answer:

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8. Let $f (x) = a x^{2} + b x + c, a \neq 0$ and $Δ = b^{2} - 4 a c$ . If $α + β$ , $α^{2} + β^{2}$ and $α^{3} + β^{3}$ are in GP, then