Which polynomial does not have x=0 as a zero?
Answer and explanation
Correct answer: x²+1
A number r is a zero of a polynomial p(x) when p(r)=0. To test x=0, substitute zero into each option. For x³−2x, the value is 0−0=0. For 5x²+x, it is 0+0=0. For x⁴, it is 0, so all three have zero as a zero. For x²+1, the value is 0²+1=1, not zero; therefore option D is the unique correct answer. The decisive feature is the constant term: at x=0, every positive-power term vanishes and the polynomial value equals its constant term. The first three expressions have constant term 0, whereas x²+1 has constant term 1.
Frequently asked questions
What is the correct answer to this question?
x²+1
Why is this the correct answer?
A number r is a zero of a polynomial p(x) when p(r)=0. To test x=0, substitute zero into each option. For x³−2x, the value is 0−0=0. For 5x²+x, it is 0+0=0. For x⁴, it is 0, so all three have zero as a zero. For x²+1, the value is 0²+1=1, not zero; therefore option D is the unique correct answer. The decisive feature is the constant term: at x=0, every positive-power term vanishes and the polynomial value equals its constant term. The first three expressions have constant term 0, whereas x²+1 has constant term 1.
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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