Question

Find the quadratic equation whose roots are twice the roots of 2x²-5x+2=0​

Answer 1

Answer:

x²-5x+4=0

Step-by-step explanation:

2$x^{2}$-5$x$+2=0

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

$\alpha =2$

$\beta =\frac{1}{2}$

given the roots of the required equation is twice the roots of the given equation

therefore, roots of the roots of the required quadratic equation are

$\alpha =4$

$\beta =1$

therefore the equation is

$x^{2} -(\alpha +\beta)x+\alpha\beta=0$

$x^{2} -5x+4$=0