Question

If alpha,beta are the roots of equation x^2-5x+6=0 and alpha > beta then the equation with the roots (alpha+beta)and (alpha-beta) is

Answer 1

Answer:

The required equation is $\bf\:x^2-6x+5=0$

Step-by-step explanation:

Given:

$\alpha\:and\:\beta$ are roots of

$x^2-5x+6=0$

$(x-3)(x-2)=0$

$x=3\:and\:2$

$\implies\:\alpha+\beta=5$

and $\alpha-\beta=1$

The equation having $\alpha+\beta$ and $\alpha-\beta$ as roots is

$x^2-(sum\:of\:the\:roots)x+(product\:of\:the\:roots)=0$

$x^2-(5+1)x+(5*1)=0$

$\implies\boxed{\bf\:x^2-6x+5=0}$ is the required equation

Answer 2

The required equation is :x^2-6x+5=0x

2

−6x+5=0

Step-by-step explanation:

Given:

\alpha\:and\:\betaαandβ are roots of

x^2-5x+6=0x

2

−5x+6=0

(x-3)(x-2)=0(x−3)(x−2)=0

x=3\:and\:2x=3and2

\implies\:\alpha+\beta=5⟹α+β=5

and \alpha-\beta=1α−β=1

The equation having \alpha+\betaα+β and \alpha-\betaα−β as roots is

x^2-(sum\:of\:the\:roots)x+(product\:of\:the\:roots)=0x

2

−(sumoftheroots)x+(productoftheroots)=0

x^2-(5+1)x+(5*1)=0x

2

−(5+1)x+(5∗1)=0

\implies\boxed{\bf\:x^2-6x+5=0}⟹

x

2

−6x+5=0

is the required equation