Q1
Factorising x²-5x+6 gives:
A(x-2)(x-3)
B(x-1)(x-6)
C(x+2)(x+3)
D(x-6)(x+1)
CBSEClass 10 (CBSE)MathematicsCh 4 · Topic 1
Solving Quadratic Equations by Factorisation
Learning to solve a quadratic equation by factoring it into two linear factors.
Core concept
For example, x²-5x+6=0 factorises into (x-2)(x-3)=0, giving two solutions: x=2 and x=3 (found by setting each factor to zero separately). Factorising requires finding two numbers that multiply to give the constant term (c) and add to give the coefficient of x (b) — for x²-5x+6, we need two numbers multiplying to 6 and adding to -5, which are -2 and -3, leading directly to the factors (x-2) and (x-3).
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• A quadratic ax²+bx+c=0 can be solved by factorising into two linear factors, each set to zero.
• Example: x²-5x+6=0 factors to (x-2)(x-3)=0, giving x=2 and x=3.
• Find two numbers multiplying to c and adding to b to determine the factors.
• This method works well when the quadratic factorises with integer/simple rational numbers.