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 zeroes of x²−9x+k are equal, what is k?MediumLevel 46Which of the following conclusions is correct when x=2 is substituted in the polynomial p(x)=x^3-4x^2+x+6?HardLevel 46If the zeroes of the polynomial \(p(x)=x^3+px^2+qx-6\) are \(1, 2\), and \(3\), what is the value of \(p+q\)?HardLevel 46If the zeroes of the polynomial \(f(x)=x^3+px^2+qx-6\) are \(1\), \(2\), and \(3\), what is the value of \(p+q\)?HardLevel 46Which of the following can be a quadratic polynomial whose zeroes are \(\frac{2}{3}\) and \(-\frac{5}{4}\)?HardLevel 46If the zeroes of the polynomial \(x^2+ax+b\) are \(4\) and \(-7\), what is the value of \(a-b\)?HardLevel 46Which polynomial has degree (4)?HardLevel 46If \(p(x)=x^2-5x+6\), what is the value of \(p(3)-p(2)\)?HardLevel 46If the sum of the zeroes of the polynomial \(p(x)=2x^2+kx+8\) is \(3\), what is the value of \(k\)?HardLevel 46If the product of the zeroes of the polynomial \(p(x)=3x^2-10x+m\) is \(\frac{4}{3}\), what is the value of \(m\)?HardLevel 46Which statement about the zeroes of (x^2-6x+9) is correct?MediumLevel 46If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?MediumLevel 46What are the zeroes of the polynomial \(x^3-6x^2+11x-6\)?HardLevel 46If \(p(x)=x^3-3x^2-4x+12\), which of the following is a factor of \(p(x)\)?HardLevel 46If \((x+1)\) is a factor of the polynomial \(2x^3+kx^2-5x+2\), what is the value of \(k\)?HardLevel 46If (x+1) is a factor of the polynomial P(x)=2x^3+kx^2-5x+2, what is the value of k?HardLevel 46What is the remainder when the polynomial x^3 - 5x^2 + 8x - 4 is divided by x - 1?HardLevel 46What is the remainder when the polynomial \(p(x)=3x^3-2x^2+x+7\) is divided by \(x+2\)?HardLevel 46If the remainder when the polynomial \(p(x)\) is divided by \(x-4\) is \(7\), what is the value of \(p(4)\)?HardLevel 46Which one is not a linear factor of (x^4-1)?HardLevel 46