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 zeros of the polynomial \(x^2+mx+n\) are \(0\) and \(5\), what is the value of \(m+n\)?HardLevel 46If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(x^2-11x+30\), what is the value of \((\alpha-\beta)^2\)?HardLevel 46If \(p(x)=4x^2-12x+9\), which statement about its zeroes is correct?HardLevel 46Which statement is correct for the polynomial \(p(x)=x^3-7x+6\)?HardLevel 46If \(x+2\) is a factor of the polynomial \(p(x)=x^3+mx^2-4x-4\), what is the value of \(m\)?HardLevel 46If (p(x)=x^2+ax+b), (p(2)=3), and (p(-1)=6), what is the value of (a+b)?HardLevel 47If (\alpha) and (\beta) are zeroes of the quadratic polynomial (x^2-6x+k) and (\alpha^2+\beta^2=20), what is the value of (k)?HardLevel 46If the degree of (p(x)=(m+2)x^5+(m-3)x^4+6x-1) is (4), what is (m)?HardLevel 48If the polynomial (p(x)=kx^3-2x^2+5x-4) satisfies (p(1)=7), what is the value of (k)?HardLevel 48What is the coefficient of \(x\) in the sum of the polynomials \(p(x)=4x^3-7x^2+2x-5\) and \(q(x)=-x^3+3x^2-6x+9\)?HardLevel 48What is the degree of the sum of (p(x)=5x^4-2x^2+1) and (q(x)=-5x^4+3x^3+x-6)?HardLevel 48If the degree of (p(x)) is (5) and the degree of (q(x)) is (2), what is the degree of non-zero (p(x)q(x))?HardLevel 48What is the coefficient of x^2 in (2x-1)(x^2-3x+4)?MediumLevel 48If (x=-2) is a zero of (p(x)=x^2+kx-8), what is (k)?HardLevel 48What is the value of p(2) for the polynomial p(x) = 3x³ − 8x² + 7x − 2?HardLevel 48For which value of \(m\) will \(p(1)=0\) for the polynomial \(p(x)=x^3-5x^2+mx+8\)?HardLevel 48For the polynomial \(p(x)=x^4-5x^2+4\), what is the value of \(p(-2)\)?HardLevel 48If \(p(x)=x^2+ax+b\), \(p(2)=0\), and \(p(4)=0\), what is the value of \(a+b\)?HardLevel 48If \(p(x)=x^2+ax+b\) is a quadratic polynomial such that \(p(-1)=0\) and \(p(5)=0\), what is the value of \(b\)?HardLevel 48If \(p(x)=ax^4+bx^3+cx^2+d\), where \(a=0\), \(b=0\), and \(c\ne 0\), what is the degree of \(p(x)\)?HardLevel 48