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Class 10MathematicsPolynomialsPolynomials in one variableExpertLevel 48
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If \(p(x)=x^2-4x+3\), which of the following values of \(x\) makes \(p(x)<0\)?

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Answer and explanation

Correct answer: 2

Factoring gives \(p(x)=(x-1)(x-3)\). The product is negative between its two roots, so \(p(x)<0\) when \(1<x<3\). Among the given choices, only \(x=2\) lies in this interval. Hence, option A is correct. Exam tip: For a quadratic with a positive leading coefficient, the expression is negative between two distinct real roots and positive outside them.

Related tags

Sign-Of-PolynomialQuadratic-PolynomialZeroesInequalities

Frequently asked questions

What is the correct answer to this question?

2

Why is this the correct answer?

Factoring gives \(p(x)=(x-1)(x-3)\). The product is negative between its two roots, so \(p(x)<0\) when \(1<x<3\). Among the given choices, only \(x=2\) lies in this interval. Hence, option A is correct. Exam tip: For a quadratic with a positive leading coefficient, the expression is negative between two distinct real roots and positive outside them.

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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