Is \(x=0\) a root of the equation \(3x^2+2x=0\)?
Answer and explanation
Correct answer: Yes
Substituting \(x=0\) gives \(3(0)^2+2(0)=0\). Hence the left-hand side is zero and \(x=0\) is a root. Alternatively factor: \(3x^2+2x=x(3x+2)=0\), giving roots \(x=0\) and \(x=-\tfrac{2}{3}\). Option (C) is incorrect because substituting \(x=2\) yields \(3(2)^2+2(2)=16\neq0\). Option (D) is wrong since the equation is explicit and substitution determines whether a value is a root. Exam tip: To check a root substitute the value into the polynomial or factor the polynomial to find all roots quickly.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
Substituting \(x=0\) gives \(3(0)^2+2(0)=0\). Hence the left-hand side is zero and \(x=0\) is a root. Alternatively factor: \(3x^2+2x=x(3x+2)=0\), giving roots \(x=0\) and \(x=-\tfrac{2}{3}\). Option (C) is incorrect because substituting \(x=2\) yields \(3(2)^2+2(2)=16\neq0\). Option (D) is wrong since the equation is explicit and substitution determines whether a value is a root. Exam tip: To check a root substitute the value into the polynomial or factor the polynomial to find all roots quickly.
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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