Question

If the roots of $x^3-k{x}^2+14x-8$ =0 are in geomatrical progression, then k =

• A. -3
• B. 7
• C. 4
• D. 0

Answer 1

Answer: (B)

7

sinx, tanx, cosx in GP

$⟹{\tan }^{2}x=\sin x\cos x⟹\sin x={\cos }^{3}x$

Above shows ${\cos }^{3}x$ plot and we know sinx plot

Hence between 0 and $2\pi$ i.i between 0 and 6.28 ther will be two solutions. One between 0 and $\pi /2$ let us call it as $\theta$ so the other solution at $\pi +\theta$

Hence the difference between solutoions is $\pi$

Option: D