The correct option is A 2 and 3
Given equation is x2−5x+6=0.
Standard form of a quadratic equation is ax2+bx+c=0
On comparing with the standard form, a=1,b=−5 and c=6.
Find the factor pair of a×c such that the numbers add up to b.
a×c = 6
Factor pairs of 6 are 1×6,2×3,−1×−6,−2×−3
Let's consider numbers -2 and -3.
(−3)×(−2)=6=a×c
(−3)+(−2)=−5=b
We now simplify the given equation,
x2−5x+6=0.
⇒x2−2x−3x+6=0
⇒x(x−2)−3(x−2)=0
⇒(x−2)(x−3)=0
⇒x=2 and x=3
∴ 2 and 3 are the roots of the given equation.