Which polynomial makes x=0 a zero?
Answer and explanation
Correct answer: 3x^3-2x
A number r is a zero of a polynomial when substituting x=r makes the polynomial equal to zero. For x=0, the value is simply the constant term, because every positive power of zero vanishes. Option A gives 0^2+5=5; option B gives 3(0)^3-2(0)=0; option C gives 0^4+1=1; and option D gives 2(0)^2-7(0)+9=9. Equivalently, option B has no constant term and can be written as x(3x^2-2), so x is a factor and zero is a zero. Thus only option B satisfies the condition.
Frequently asked questions
What is the correct answer to this question?
3x^3-2x
Why is this the correct answer?
A number r is a zero of a polynomial when substituting x=r makes the polynomial equal to zero. For x=0, the value is simply the constant term, because every positive power of zero vanishes. Option A gives 0^2+5=5; option B gives 3(0)^3-2(0)=0; option C gives 0^4+1=1; and option D gives 2(0)^2-7(0)+9=9. Equivalently, option B has no constant term and can be written as x(3x^2-2), so x is a factor and zero is a zero. Thus only option B satisfies the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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