If \(p(x)=4x^2-12x+9\), which statement about its zeroes is correct?
Answer and explanation
Correct answer: Both zeroes are \(\frac{3}{2}\)
Factoring gives \(4x^2-12x+9=(2x-3)^2\). Hence \(2x-3=0\), so \(x=\frac{3}{2}\), and this zero is repeated; therefore, both zeroes are \(\frac{3}{2}\). Option C is incorrect because it treats the zeroes as two distinct values. Exam tip: A quadratic polynomial that is a perfect square, or has discriminant zero, has equal zeroes.
Frequently asked questions
What is the correct answer to this question?
Both zeroes are \(\frac{3}{2}\)
Why is this the correct answer?
Factoring gives \(4x^2-12x+9=(2x-3)^2\). Hence \(2x-3=0\), so \(x=\frac{3}{2}\), and this zero is repeated; therefore, both zeroes are \(\frac{3}{2}\). Option C is incorrect because it treats the zeroes as two distinct values. Exam tip: A quadratic polynomial that is a perfect square, or has discriminant zero, has equal zeroes.
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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