Question

if α;β arethe roots of the equation x^2-5x+6=0;the equation with roots (α+β)and(α-β)is​

Answer 1

Answer:

I don't know

I don't know

Answer 2

Given:-

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

To Find:-

• the equation with roots (α+β)and(α-β)

Solution:-

α and β are Roots Of the Equation

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

$= > {x}^{2} - 2x - 3x+ 6 = 0$

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

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

$x = 3 \: and \: 2$

From here,

$\alpha = 3$

$\beta = 2$

$= > \alpha + \beta = 5$

and

$= > \alpha - \beta = 1$

The equation having α+β and α-β as roots is

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

$= > {x}^{2} - (5 + 1)x + (5 \times1) = 0$

$= > {x}^{2} - 6x + 5 = 0$

Is the required equation