Question

if the roots of x²-5x+6=0 are alpha and beta, then the equation of roots alpha/2, beta/2.​

Answer 1

Answer:

x²-5x+6 = 0

Factor the middle term as :

x²-2x-3x+6=0

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

x = 2,3

Therefore

alpha-beta =6

Answer 2

$\large \sf \underbrace{ \underline{Solution+Explanation}}$

First we have to find roots of equation

➠x²-5x+6

➠x²-2x-3x+6

➠x(x-2)-3(x-2)

➠(x-3)(x-2)

So roots are 3 and 2

which means a=3 and b=2

$\sf We \: have \: to \: find \: equation \: of \: roots \: \frac{a}{2} and \: \frac{b}{2}$

$\sf i.e. \frac{3}{2} \: and \: \frac{2}{2}$

As we know that formula to find quadratic equation using roots is

x²-(sum)x+product

$\sf ➠\:\:x²-(\frac{3}{2}+1)x+(\frac{3}{2}×1)=0$

$\sf➠\:\: x²-(\frac{3+2}{2})x+\frac{3}{2}=0$

$\sf ➠\:\:x²-(\frac{5}{2})x+\frac{3}{2}=0$

$\sf multiply\: this\: equation \:by\: 2$

➠ 2x²-5x+3=0

So this is the required equation.