Question

The quadratic equation whose roots are twice the roots of $2x^2-5x+2=0$ is:

• A. $8x^2-10x+2=0$
• B. $x^2-5x+4=0$
• C. $2x^2-5x+2=0$
• D. $x^2-10x+6=0$
• E. none of the above

Answer 1

Answer: (B)

Let the roots of the equation $2x^2-5x+2=0$ are $\alpha$ and $\beta$ . Then $\alpha +\beta =\frac{5}{2}$ and $\alpha \beta =1$ Now, the roots of required equation be $2\alpha$ and $2\beta$ . $\therefore$ Sum of roots $=2(\alpha +\beta )=5$ and product of roots $=2\alpha .2\beta$ $=4\alpha \beta$ $=4$ $\therefore$ Required equation is $x^2-5x+4=0$