If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(ax^2+bx+c=0\), what is \(\alpha\beta\) equal to?
Answer and explanation
Correct answer: \frac{c}{a}
Divide the equation by \(a\) (assuming \(a\neq 0\)) to get \(x^2+\frac{b}{a}x+\frac{c}{a}=0\). Comparing with \(x^2-(\alpha+\beta)x+\alpha\beta=0\) gives \(\alpha\beta=\frac{c}{a}\). Option B has the wrong sign; options C and D confuse the coefficient \(b\) with the constant term. Exam tip: product of roots = constant term ÷ leading coefficient, and sum of roots = -(middle coefficient) ÷ leading coefficient.
Frequently asked questions
What is the correct answer to this question?
\frac{c}{a}
Why is this the correct answer?
Divide the equation by \(a\) (assuming \(a\neq 0\)) to get \(x^2+\frac{b}{a}x+\frac{c}{a}=0\). Comparing with \(x^2-(\alpha+\beta)x+\alpha\beta=0\) gives \(\alpha\beta=\frac{c}{a}\). Option B has the wrong sign; options C and D confuse the coefficient \(b\) with the constant term. Exam tip: product of roots = constant term ÷ leading coefficient, and sum of roots = -(middle coefficient) ÷ leading coefficient.
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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