Which of the following values is a zero of the polynomial \(p(x)=4x^2-12x+9\)?
Answer and explanation
Correct answer: \(\frac{3}{2}\)
The polynomial can be factorised as \(p(x)=(2x-3)^2\). Thus, \(p(x)=0\) when \(2x-3=0\), giving \(x=\frac{3}{2}\). Indeed, \(p\left(\frac{3}{2}\right)=9-18+9=0\), whereas the other options do not make the polynomial zero. Exam tip: For a quadratic polynomial, try factorisation before substituting every option.
Frequently asked questions
What is the correct answer to this question?
\(\frac{3}{2}\)
Why is this the correct answer?
The polynomial can be factorised as \(p(x)=(2x-3)^2\). Thus, \(p(x)=0\) when \(2x-3=0\), giving \(x=\frac{3}{2}\). Indeed, \(p\left(\frac{3}{2}\right)=9-18+9=0\), whereas the other options do not make the polynomial zero. Exam tip: For a quadratic polynomial, try factorisation before substituting every option.
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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