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Question

The roots of the quadratic equation x2−5x+6=0 are .

A
2 and 3
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B
-2 and -3
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C
-1 and -6
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D
1 and 6
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Solution

The correct option is A 2 and 3
Given equation is x25x+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,
x25x+6=0.
x22x3x+6=0
x(x2)3(x2)=0
(x2)(x3)=0
x=2 and x=3
2 and 3 are the roots of the given equation.

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