Under what condition is \(x=0\) a root of the quadratic equation \(ax^2+bx+c=0\)?
Answer and explanation
Correct answer: \(c=0\)
Substitute \(x=0\) into \(ax^2+bx+c=0\): this gives \(c=0\). Therefore \(x=0\) is a root only when the constant term \(c\) is zero. If \(c=0\), the equation reduces to \(ax^2+bx=0\) or \(x(ax+b)=0\), so \(x=0\) is indeed a root. Option B is incorrect because \(a=0\) makes the equation linear (not necessarily giving zero as a root); option C (\(b=0\)) does not ensure zero is a root unless \(c=0\) also; option D (\(a=b\)) is irrelevant to whether zero is a root. Exam tip: always test a suspected root by direct substitution into the equation.
Frequently asked questions
What is the correct answer to this question?
\(c=0\)
Why is this the correct answer?
Substitute \(x=0\) into \(ax^2+bx+c=0\): this gives \(c=0\). Therefore \(x=0\) is a root only when the constant term \(c\) is zero. If \(c=0\), the equation reduces to \(ax^2+bx=0\) or \(x(ax+b)=0\), so \(x=0\) is indeed a root. Option B is incorrect because \(a=0\) makes the equation linear (not necessarily giving zero as a root); option C (\(b=0\)) does not ensure zero is a root unless \(c=0\) also; option D (\(a=b\)) is irrelevant to whether zero is a root. Exam tip: always test a suspected root by direct substitution into the equation.
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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