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 (p(x)=x^2-5x+6) are (\alpha,\beta), what is ((\alpha-\beta)^2)?ExpertLevel 46If (\alpha+\beta=6) and (\alpha\beta=8), which monic polynomial has zeroes (\alpha+1) and (\beta+1)?ExpertLevel 46If the graph of a polynomial cuts the (x)-axis at (x=-2), (x=0), and (x=3), which is the monic polynomial of least degree?ExpertLevel 46If \(x=1\) is a zero of \(p(x)=x^3+x^2-10x+8\), what is the remaining quadratic factor?ExpertLevel 46If p(x)=2x^3+3x^2-8x+3 , what is the remainder when p(x) is divided by x-1 ?ExpertLevel 46If \(p(x)=x^3-2x^2-5x+6\), what is the value of \(p(3)\)?ExpertLevel 46Which statement is correct for (p(x)=0), where (p(x)) is the zero polynomial?ExpertLevel 46Which of the following is a constant polynomial?ExpertLevel 46If (p(x)=\sqrt{5}x^3-\frac{2}{3}x+1), what type of polynomial is it?ExpertLevel 46Which of the following is a linear polynomial in x?EasyLevel 46If \(p(x)=ax+b\) with \(a\ne0\), what is its zero?ExpertLevel 46If \(p(x)=4x-12\), what is its zero?ExpertLevel 46If x=0 is a zero of p(x)=7x^3-2x, what is the reason?EasyLevel 46If \(p(x)=x^2+1\), which statement about its zeroes in the real numbers is correct?ExpertLevel 46Which polynomial has 8-19 and 849 as its zeroes?ExpertLevel 46If the sum and product of the zeroes of \(p(x)=x^2-ax+a\) are equal and \(a\ne0\), what can be the value of \(a\)?ExpertLevel 46If both zeroes of (p(x)=2x^2+kx+8) are equal, what is the value of (k^2)?ExpertLevel 46If one zero of (p(x)=x^2+kx+16) is twice the other and both are positive, what is (k)?ExpertLevel 46If one zero of the polynomial \(p(x)=x^2-10x+r\) is \(4\), what is its other zero?ExpertLevel 46If one zero of the polynomial \(p(x)=x^2+3x-18\) is \(3\), what is its other zero?ExpertLevel 46