Question

please solve this question​

Answer 1

VERIFIED ANSWER ‼️

x2−5x+6=0…(i)

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52Or, (α−β)2+4αβ=−(−5)=25

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52Or, (α−β)2+4αβ=−(−5)=25Or, (α−β)2+4×6=25

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52Or, (α−β)2+4αβ=−(−5)=25Or, (α−β)2+4×6=25Or, (α−β)2+24=25

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52Or, (α−β)2+4αβ=−(−5)=25Or, (α−β)2+4×6=25Or, (α−β)2+24=25Or, (α−β)2=25−24=1

x2−5x+6=0…(i) If α and β are two solution of ax2+bx+c=0 then α+β=−ba and αβ=ca.So from equation (i) and using above we can write α+β=−(−5)=5 and αβ=6.Now α+β=5Or, (α+β)2=52Or, (α−β)2+4αβ=−(−5)=25Or, (α−β)2+4×6=25Or, (α−β)2+24=25Or, (α−β)2=25−24=1Or, α−β=± 1(Answer)

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.