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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 the degree of (p(x)=mx^3+(m-1)x^2+2x+1) is (2), what is (m)?HardLevel 47If (p(x)=3x^2-2x+1), what is (p(x)+p(-x))?HardLevel 47If p(x) = x³ − 4x, what is the value of p(−2) + p(2)?HardLevel 47For which value of \(x\) does the polynomial \(p(x)=x^2+4x+5\) attain its minimum value?HardLevel 47For a real number \(x\), what is the minimum value of \(p(x)=x^2-6x+10\)?HardLevel 47If \(p(x)=x^2+kx+9\) is a perfect-square polynomial and \(k>0\), what is the value of \(k\)?HardLevel 47Which of the following polynomials can be expressed as the square of a binomial?HardLevel 47If \(p(x)=x^3-3x^2+3x-1\), what is the value of \(p(2)\)?HardLevel 47What is the product of p(1) and p(−1) for p(x)=2x³+x²−5x+2?MediumLevel 47For (p(x)=2x^3+x^2-5x+2), what is the difference (p(2)-p(-1))?HardLevel 47If \\(f(x)=x^2+px+q\\) is a quadratic polynomial and \\(f(0)=6\\) and \\(f(2)=0\\), what is the value of the coefficient \\(p\\)?HardLevel 47If \(p(x)=x^3+ax^2+bx\) satisfies \(p(0)=0\), which of the following conclusions is certainly correct?HardLevel 47Which polynomial does not have x=0 as a zero?EasyLevel 47If \(p(x)=x^2-2x+3\), what is \(p(x+1)\)?HardLevel 47If \(p(x)=2x^2+3x-4\), what is \(p(2x)\)?HardLevel 47If p(x)=x²−4x+1, what is p(x)−p(1)?MediumLevel 47In the polynomial (p(x)=ax^3+bx^2+cx+d), (a\ne0). Why is it wrong to call (p(x)) a linear polynomial?HardLevel 46If \(2\) is a zero of the polynomial \(p(x)=kx^2-5x+6\), what is the value of \(k\)?HardLevel 46If the zeroes of the polynomial \(p(x)=x^2-(m+3)x+12\) are 3 and 4, what is the value of \(m\)?HardLevel 46What is the product of the zeroes of the quadratic polynomial \(2x^2-7x+3\)?HardLevel 46