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 \(p(x)=x^2-2x-8\), what are the zeroes of \(p(x+3)\)?ExpertLevel 48A non-zero polynomial in one variable has degree 4. What is the maximum number of zeroes it can have?ExpertLevel 48If (p(x)=ax^2+bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?ExpertLevel 48If the zeroes of the polynomial \(p(x)=x^2-kx+36\) are positive and in the ratio 1:4, what is the value of k?ExpertLevel 48If p(x) = 2x² − 7x + 5, what is the difference between the sum and product of its zeroes?MediumLevel 48If the value of the polynomial (p(x)=x^3+mx-10) at (x=2) is zero, what is the value of (m)?ExpertLevel 48If \(p(x)=x^2+4x+4\), what is the value of \(p(-2+h)\)?ExpertLevel 48If the zeroes of (p(x)=x^3+px^2+qx+15) are (-1,3,-5), what is (p+q)?ExpertLevel 48If (p(x)=x^2-12x+35), what is (\frac{1}{\alpha-1}+\frac{1}{\beta-1}), where (\alpha,\beta) are zeroes?ExpertLevel 48Which of the following expressions is a polynomial in one variable \(x\) of degree 4?ExpertLevel 48If (p(x)=5x^2-20x+20), what is the sum of its zeroes?ExpertLevel 48If \(x^2+4\) is a factor of the polynomial \(p(x)=x^4-16\), what contribution does this factor make to the real zeroes of \(p(x)\)?ExpertLevel 48If \(p(x)=x^2+ax+a\) and \(p(1)=0\), what is the value of \(a\)?ExpertLevel 48If the minimum value of \(p(x)=x^2-2x+k\) is \(3\), what is the value of \(k\)?ExpertLevel 48If \(p(x)=x^2-4x+3\), which of the following values of \(x\) makes \(p(x)<0\)?ExpertLevel 48If \(p(x)=x^3-3x^2-4x+12\), what is its complete factorised form?ExpertLevel 48If \(p(x)=x^2+5x+6\) and \(r(x)=p(-x)\), what are the zeroes of \(r(x)\)?ExpertLevel 48If (p(x)=x^2-7x+12), at which points will the graph of (p(x)) cut the (x)-axis?ExpertLevel 48If the polynomial p(x) = x² + 2x + c has no real zero, which condition on c is correct?ExpertLevel 48If p(x) = x² − 6x + 8, which monic polynomial has the squares of its zeroes as its zeroes?HardLevel 48