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

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. None

E. None of the above

Answer: B. $x^2 - 5x + 4 = 0$

Let α and β be the roots of the given equation.
Then, α + β = $5/2$ and αβ = $2/2$ = 1
.`. 2α + 2β
.`. 2(α + β)
.`. 5,(2α)(2β) = 4
So, the requiared equation is :
$x^2 - 5x + 4 = 0$

Posted in: Quadratic Equations - Algebra - Mathematics