Question

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

• A. $ 8{{x}^{2}}-10x+2=0 $
• B. $ {{x}^{2}}-5x+4=0 $
• C. $ 2{{x}^{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 $ 2{{x}^{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 $