Which of the following quadratic equations has roots -2 and 6?
Answer and explanation
Correct answer: \(x^2-4x-12=0\)
If a quadratic has roots α and β, it can be written as \((x-α)(x-β)=0\). With roots -2 and 6 we get \((x+2)(x-6)=0\). Expanding gives \(x^2-4x-12=0\), so option A is correct. For comparison, option C expands to \((x-2)(x-6)=x^2-8x+12\) which has roots 2 and 6, so it is wrong. Exam tip: check sum and product of roots quickly — for a monic quadratic \(x^2+bx+c\), sum of roots = -b and product = c; here sum = -2+6=4 (so \(b=-4\)), product = -12.
Frequently asked questions
What is the correct answer to this question?
\(x^2-4x-12=0\)
Why is this the correct answer?
If a quadratic has roots α and β, it can be written as \((x-α)(x-β)=0\). With roots -2 and 6 we get \((x+2)(x-6)=0\). Expanding gives \(x^2-4x-12=0\), so option A is correct. For comparison, option C expands to \((x-2)(x-6)=x^2-8x+12\) which has roots 2 and 6, so it is wrong. Exam tip: check sum and product of roots quickly — for a monic quadratic \(x^2+bx+c\), sum of roots = -b and product = c; here sum = -2+6=4 (so \(b=-4\)), product = -12.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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