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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

For which value will (p(x)=(m-2)x^4+3x^2+x+1) have degree not more than (2)?ExpertLevel 46If \(p(x)=x^3-3x^2+3x-1\), what is the value of \(p(x)\) at \(x=1\)?ExpertLevel 46If \(p(x)=x^2-9\), which are the zeroes of \(p(x)\)?ExpertLevel 46If \(p(x)=x^2+6x+9\), what is the nature of its zeroes?ExpertLevel 46If p(x)=2x^2-7x+3, what is the sum of its zeroes?MediumLevel 46If p(x)=5x^2+2x-8, what is the product of its zeroes?MediumLevel 46If the zeroes of a quadratic polynomial are (2) and (5), what is one monic polynomial?ExpertLevel 46If the sum of the zeroes of a monic quadratic polynomial is -4 and their product is 7, which is the polynomial?ExpertLevel 46If the zeroes of (p(x)=x^2-(k+2)x+3k) are (3) and (k), which statement is correct?ExpertLevel 46If (2 ) and (-1 ) are zeroes of (p(x)=ax^2+bx+c ), what is the value of (\frac{b}{a} )?ExpertLevel 46If \(p(x)=x^3-4x^2+x+6\), which of the following is a zero of \(p(x)\)?ExpertLevel 46If p(x) = x³ − 6x² + 11x − 6, what are the zeroes of p(x)?ExpertLevel 46If p(x) = x^3 + 3x^2 - 4x - 12, which of the following is a factor of p(x)?ExpertLevel 46If (p(x)=4x^2-12x+9), what is the nature of its zeroes?ExpertLevel 46If the zeroes of the polynomial \(p(x)=x^2+px+q\) are 4 and −5, what is the value of \(p+q\)?ExpertLevel 46If the sum of the zeroes of p(x)=x^2-2(k+1)x+k^2 is 10, what is k?MediumLevel 46If the sum of zeroes of (p(x)=3x^2+(m-1)x-2) is (0), what is (m)?ExpertLevel 46If the product of zeroes of (p(x)=kx^2-6x+4) is (2), what is (k)?ExpertLevel 46If (p(x)=x^2-8x+15), what is the sum of squares of its zeroes?ExpertLevel 46If (p(x)=2x^2-9x+4), what is (\frac{1}{\alpha}+\frac{1}{\beta}), where (\alpha,\beta) are zeroes?ExpertLevel 46