If \(x=0\) is a root of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), which of the following conditions must be true?
Answer and explanation
Correct answer: \(c=0\)
Substitute the proposed root into the equation: \(a(0)^2+b(0)+c=0\), which gives \(c=0\). Thus the constant term must be zero. Neither \(b=0\) nor \(a+b=0\) is necessary, while \(a=0\) would make the equation non-quadratic. Exam tip: If zero is a root of a polynomial, its constant term is always zero.
Frequently asked questions
What is the correct answer to this question?
\(c=0\)
Why is this the correct answer?
Substitute the proposed root into the equation: \(a(0)^2+b(0)+c=0\), which gives \(c=0\). Thus the constant term must be zero. Neither \(b=0\) nor \(a+b=0\) is necessary, while \(a=0\) would make the equation non-quadratic. Exam tip: If zero is a root of a polynomial, its constant term is always zero.
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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