List of top Mathematics Questions on Quadratic Equation

If \(\alpha,\beta\) are the roots of \(ax^2+bx+c=0\), then \[ \left(\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\right)^2 = \]

A train travels $400 \text{ km}$ at a uniform speed. If the speed had been $10 \text{ km/h}$ more, it would have taken $2$ hours less for the same journey, then the speed of the train is _____.

The graphical representation of a quadratic polynomial $ax^2 + bx + c$ is a _____.

Let N be the number of quadratic equations with coefficients from {0,1,2,...,9} such that 0 is a solution of each equation. Then the value of N is:

If \(P(x) = ax^2 + bx + c\) and \(Q(x) = -ax^2 + dx + c\) where \(ac \neq 0\), then \(P(x) \cdot Q(x) = 0\) has:

If \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]

The equation \(2x^5 + 5x = 3x^3 + 4x^4\) has:

If the quadratic equation \( ax^2 + bx + c = 0 \) (\( a > 0 \)) has two roots \( \alpha \) and \( \beta \) such that \( \alpha < -2 \) and \( \beta > 2 \), then:

If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:

If \(\frac{x+y}{x-y}+\frac{x-y}{x+y}=\frac{10}{3}\),then \(\frac xy=\)

If a quadratic equation \(2x^2 + kx+3=0\) have two equal roots then \(k=\)

If the equation \(ax^2-8x+4=0\) has equal roots then \(a=\) ____ .

If \(α, β\) are the roots of a quadratic equation \(ax^2+bx+c=0,\ a≠0\) then \(α^2+β^2\)

The sum of roots of a quadratic equation \(3x^2 -7x+11=0\) is

The roots of a quadratic equation \(x^2-3x-10=0\) are

The degree of a quadratic equation \(ax^2+bx+c=0, \ a≠0\) is

If the roots of \(2x^2+kx+3=0\) are real and equal, then \(k=\)

\(8x^2-6x-9=\) _____ .