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 \(p(x)=x^2-2x+5\), what is the value of \(p(1)\), and is \(1\) a zero of this polynomial?HardLevel 46If the zeroes of a quadratic polynomial are \(\alpha\) and \(\beta\), and \(\alpha+\beta=5\) and \(\alpha\beta=6\), which monic polynomial has these zeroes?HardLevel 46If (\alpha) and (\beta) are zeroes of (2x^2-3x-5), what is (\frac{1}{\alpha}+\frac{1}{\beta})?HardLevel 46For the polynomial \(p(x)=2x^3-3x^2-11x+6\), a student finds that \(p(3)=0\) and concludes that \(x+3\) is a factor. What is the correct correction to the student's conclusion?HardLevel 46If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(3x^2+2x-1\), what is the value of \((\alpha+\beta)^2\)?HardLevel 46If the zeroes of (x^2+px+16) are equal and negative, what is (p)?MediumLevel 46If \(p(x)=x^2-4x+k\) and \(p(1)=p(3)\), what can be said about \(k\)?HardLevel 46Which of the following is a factor of the polynomial P(x) = 2x³ − 9x² + 13x − 6?HardLevel 46If p(x)=x^3-2x^2-5x+6, which of the following is not a zero?MediumLevel 46If alpha and beta are zeroes of x^2+5x+6, what is the new polynomial whose zeroes are alpha+1 and beta+1?HardLevel 46If (\alpha) and (\beta) are zeroes of (x^2-4x+1), what is (\alpha^3+\beta^3)?HardLevel 46For which (k) does (x^2+kx+9) have one zero three times the other and both positive?HardLevel 46If \(\alpha\) and \(\beta\) are the zeroes of \(x^2-8x+k\) and \(\alpha-\beta=2\), what is the value of \(k\)?HardLevel 46The sum of the zeroes of the quadratic polynomial \(kx^2+6x+4\) is \(-3\). What is the value of \(k\)?HardLevel 46If the zeroes of the polynomial \(x^2-10x+q\) are \(2r\) and \(3r\), what is the value of \(q\)?HardLevel 46If the zeroes of p(x) = x³ + ax² + bx + 8 are −1, −2, and −4, what is the value of a + b?HardLevel 46If (\alpha) and (\beta) are zeroes of (x^2-3x-10), what is (\alpha^2\beta+\alpha\beta^2)?HardLevel 46If 2x^2+5x-3 is written with factors involving (x-alpha)(x-beta), what is alpha+beta?MediumLevel 46Which of the following monic cubic polynomials has 0, 2, and −3 as its zeroes?HardLevel 46If p(x)=x^4-5x^2+4, which value is not a zero of p(x)?MediumLevel 46