EduGoog

Solution of quadratic equations, Relation between roots and coefficients (only real roots to be considered). Practical problem on quadratic equations.

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

Option:
A. $8x^2 - 10x + 2 = 0$
B. $x^2 - 5x + 4 = 0$
C. $2x^2 - 5x + 2 = 0$
D. None
Answer: B . $x^2 - 5x + 4 = 0$

Justification:

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 :
$x^2 - 5x + 4 = 0$

Back to Algebra