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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 p(x) = 5x^2 - 4x + 3, what is p(x) + p(-x)?MediumLevel 48If \(p(x)=3x^3-12x\), what is the value of \(p(-2)+p(2)\)?ExpertLevel 47For the polynomial \(p(x)=x^2-12x+40\), at which value of \(x\) is the minimum value attained?ExpertLevel 47If \(x\) is a real number, what is the minimum value of \(p(x)=x^2+14x+53\)?ExpertLevel 47If \(p(x)=x^2+kx+25\) is a perfect-square polynomial and \(k<0\), what is the value of \(k\)?ExpertLevel 47If \(p(x)=x^3-6x^2+12x-8\), what is the value of \(p(5)\)?ExpertLevel 47If \(p(x)=x^3-3x^2-4x+12\), what is the product of \(p(2)\) and \(p(-2)\)?ExpertLevel 47For p(x) = x^3 - x^2 - 4x + 4, what is p(2) - p(-2)?MediumLevel 48If \(P(x)=x^2+px+q\), \(P(0)=12\), and \(P(3)=0\), what is the value of the coefficient \(p\)?ExpertLevel 47If the polynomial \(p(x)=x^5+ax^3+b\) satisfies \(p(0)=0\), which of the following conclusions is certainly correct?ExpertLevel 47Which polynomial makes (x=0) a zero but is not the zero polynomial?ExpertLevel 47If \(p(x)=x^2-2x+4\), what is the polynomial expression for \(p(x+3)\)?ExpertLevel 47If \(p(x)=4x^2-3x+2\), what is \(p(3x)\)?ExpertLevel 47If \(p(x)=x^2-8x+15\), what is the simplified form of \(p(x)-p(3)\)?ExpertLevel 47If (p(x)=x^3+ax^2+bx+20), (p(1)=0), and (p(-4)=0), what is the value of (a-b)?ExpertLevel 47If (p(x)=2x^2-7x+3), what will (p(x+1)-p(x-1)) be?ExpertLevel 47If (x-3) is a factor of (p(x)=x^3-5x^2+ax+12), what is the value of (a)?ExpertLevel 48If (p(x)=2x^3+kx^2-11x+5) leaves remainder (7) when divided by (x+1), what is (k)?ExpertLevel 48If the zeroes of (p(x)=x^2-(m+4)x+4m) are (4) and (m), which statement is correct?ExpertLevel 48If both zeroes of (p(x)=x^2+rx+9) are equal and negative, what is the value of (r)?ExpertLevel 48