If α, β are two real roots of a quadratic equation ax2+bx+c=0 and α+β,α2+β2,α3+β3 are in GP, then which of the following is correct?a) Δ≠0b) bΔ=0c) cΔ=0d) Δ=0

Question

If α, β are two real roots of a quadratic equation ax2+bx+c=0 and α+β,α2+β2,α3+β3 are in GP, then which of the following is correct?a) Δ≠0b) bΔ=0c) cΔ=0d) Δ=0

icebox2686zsd · Accepted Answer

Step 1α4+β4+2α2β2=α4+β4+αβ3+βα32α2β2=αβ3+βα32α2β2=αβ(α2+β2)αβ(α2+β2−2αβ)=0αβ(α−β)2=0Now this is where you got problem . You cannot cancel αβ from both sides as we are not sure that they will be non-zero.Continuing furtherca⋅Δa2=0using the fact that αβ=ca and |α−β|=Δ|a|therefore , now since we are sure that a≠0 we can cancel a3 from both sidesc) Δ=0 which is same as you got.

Felicity Carter · Accepted Answer

Step 1You at some point got toαβ(α−β)2=0But you aren&#039;t allowed to cancel the factor αβ at that point, since it might be zero. In other words you don&#039;t really arrive atα=β

If \alpha,\ \beta are two real roots of a quadratic

Answered question

Answer & Explanation

New Questions in Algebra I