Question

If$x^3-k^2{x}^2+(6k+5)x-5k=0$has two roots 3 and 5, then find the value of the third root

• A. 1
• B. 2
• C. 3
• D. 4
• E. none of these

Answer 1

The correct option is A 1

Soln:

Assume$\alpha$be the 3rd root.

Sum of the roots, i.e.,$3+5+\alpha =k^2$

Product of the roots, i.e.$3\times 5\times \alpha =5k$

So,$8+\alpha =9{\alpha }^2$

Then,$\alpha =-10r-\frac{8}{9}$

Hence the 3rd root is 1. Hence option (a)