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Subjects

Mathematics

Polynomials in one variable

एक चर वाले बहुपद

In this Class 10 Mathematics topic from the chapter “Polynomials,” students study algebraic expressions involving a single variable, such as x. They learn to identify a polynomial and its degree, understand constant, linear, quadratic, and cubic forms, and find its zeroes or roots. The topic also develops understanding of the relationship between zeroes and coefficients, helping students interpret polynomial equations and solve related problems accurately.

Practice questions

If (\alpha) and (\beta) are zeroes of (3x^2-10x+7), what is the value of (\alpha^2+\beta^2)?ExpertLevel 48If p(x) = x^3 - 2x^2 - 13x - 10, which of the following is a zero of p(x)?MediumLevel 48If (x=2) and (x=-3) are zeroes of (p(x)=ax^2+bx+c), what is (\frac{c}{a})?ExpertLevel 48If the difference between the two zeroes of the polynomial \(p(x)=x^2-6x+s\) is 2, what is the value of \(s\)?ExpertLevel 48If (p(x)=2x^2-5x-3), what is (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}), where (\alpha,\beta) are zeroes?ExpertLevel 48If p(x) = x³ − 4x² − 7x + 10 and (x − 1) is a factor, what is the remaining quadratic factor?MediumLevel 48If \(p(x)=(k-3)x^5+2x^3-x+9\) has degree \(3\), what is the value of \(k\)?ExpertLevel 48If (\alpha,\beta) are zeroes of (x^2-9x+20), what is the value of ((\alpha+2)(\beta+2))?ExpertLevel 48If (p(x)=x^2-4x+1), what is the sum of reciprocals of its zeroes?ExpertLevel 48If the zeroes of a quadratic polynomial are \((2+\sqrt{3})\) and \((2-\sqrt{3})\), which is the monic polynomial?ExpertLevel 48If \(p(x)=x^3-6x^2+12x-8\), what are the zero of \(p(x)\) and its multiplicity?ExpertLevel 48If \(p(x)=3x^2-12x+15\), what is the correct conclusion about its real zeroes?ExpertLevel 48If the zeroes of p(x) = x² + bx + 16 are reciprocals of each other, what can be said about b?MediumLevel 48If (p(x)=x^2-11x+30) and (q(x)=p(x-2)), what are the zeroes of (q(x))?ExpertLevel 48If \(p(x)=x^2-3x-28\), what is the distance between the zeroes of \(p(x)\)?ExpertLevel 48If one zero of the polynomial \(p(x)=2x^2+mx+18\) is \(3\), what is its other zero?ExpertLevel 48If (p(x)=4x^2-4x+1), what are its zeroes?ExpertLevel 48If \(p(x)=x^4-5x^2+4\), what are its real zeroes?ExpertLevel 48If the zeroes of (p(x)=x^3+ax^2+bx-12) are (1,3,-4), what is (a+b)?ExpertLevel 48If \(p(x)=x^3-9x\), how many distinct real zeroes does it have?ExpertLevel 48