CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
What are the roots of the quadratic equation x² − 7x + 12 = 0?
The roots are 3 and 4. The expression factorises as (x − 3)(x − 4) because the two numbers multiply to 12 and add to 7. Setting each factor to zero gives x = 3 and x = 4, and both satisfy the original equation.
- A3 and 4Correct
- B−3 and −4
- C2 and 6
- D1 and 12
Explanation
Split the middle term: x² − 3x − 4x + 12 = x(x − 3) − 4(x − 3) = (x − 3)(x − 4). So x = 3 or 4. The pair −3 and −4 would give the sum −7, which is the wrong sign.
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