The Quadratic.

Algebra Level 2

Consider two quadratic equations k x 2 − 5 x + 3 = 0 kx^2-5x+3=0 and 27 x 2 − 30 x + 8 = 0 27x^2-30x+8=0 having roots α , β \alpha,~\beta and γ , δ \gamma,~\delta respectively. If α , β , γ , δ \alpha,~\beta,~\gamma,~\delta form a geometric progression, find the value of k k .


The answer is 2.

Omkar Kulkarni by Omkar Kulkarni , 22, India

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1 solution

Raj Rajput
Jul 18, 2015

3 Helpful 0 Interesting 0 Brilliant 0 Confused

In response to Raj Rajput.

Please clarify my doubt.The solutions of the quadratics may not be in the same order.i.e delta can be 2/3 and gamma can be 4/9

Bala vidyadharan - 5 years, 11 months ago

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when we take delta to be 2/3 and gamma to be 4/9 , our common ratio of G.P comes out to be 3/2 . Now when we solve similarly as above after substituting the value of r=3/2 , we get a=1 . Substitute the value of a and r in any one eqn we get k=2.

RAJ RAJPUT - 5 years, 11 months ago

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Thanks !!!

Bala vidyadharan - 5 years, 10 months ago

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@Bala Vidyadharan – welcome :)

RAJ RAJPUT - 5 years, 10 months ago

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