Question

If alpha and beta are the roots of the equation x square - 2 x + 3 equals to zero then the equation whose roots are alpha + 2 and beta + 2

Answer 1

Answer:

$x^2-6x+11=0$ is the required equation

Step-by-step explanation:

$\alpha$ and $\beta$ are roots for the equation $x^{2}-2x+3=0$
Therefore, $\alpha +\beta =2$
and $\alpha .\beta =3$

Any quadratic equation can be expressed in the form
$x^2-Sx+P=0$

Here, S represents the Sum of the roots and P represents the product of the roots.

For a quadratic equation with roots as $\alpha +2$ and $\beta +2$

$S'=\alpha +2+\beta +2$

$P'=(\alpha +2)(\beta +2) \\ P'=\alpha .\beta +2(\alpha +\beta )+4$

Substitute the values for $\alpha +\beta$ and $\alpha .\beta$ from the first eqution.

$S'=6$ and $P'=11$

So, our required equation with roots as $\alpha +2$ and $\beta +2$ becomes:-

$x^{2}-S'x+P'=0$
$x^2-6x+11=0$