Quadratic Equations Questions - JEE

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$ is:

Find the number of positive integral values of $k$ for which $kx^2+(k-3)x+1<0$ for at least one positive $x$.

Let $\alpha,\beta$ be the roots of the quadratic equation $12x^2-20x+3\lambda=0$, $\lambda\in\mathbb{Z}$. If $\dfrac{1}{2}\leq|\beta-\alpha|\leq\dfrac{3}{2}$, then the sum of all possible values of $\lambda$ is:

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 - 2x^2 + 6x - 1 = 0$, then find the value of $\displaystyle\sum \alpha\left(\frac{\alpha^2+\alpha+1}{\alpha^2-\alpha+1}\right)$.

If α and β are the roots of the equation 2x2 + 3x + 4 = 0, then the equation whose roots are α2 and β2, is

If $-3 \leq \dfrac{x^2 - \lambda x - 2}{x^2 + x + 1} \leq 2$ for all $x \in R$, then how many integral values of $\lambda$ exist?

Let $\alpha,\beta$ be roots of $x^2-3x-\sqrt7=0$ and $\alpha^2+\frac1\beta,\beta^2+\frac1\alpha$ be roots of $x^2+px+q=0$. For $x^2+p^2qx-(11q+p)=0$, roots are

If the parabola $y=ax^2+bx+c$ has vertex at $(4,2)$ and $\lambda\in[1,3]$, and the maximum value of product $abc$ is $\lambda$, then $\dfrac{|\lambda|}{24}$ is

If $\sin\theta$ and $\cos\theta$ are the roots of the quadratic equation $ax^2 + bx + c = 0$ ($ac \neq 0$). Then find the value of $\frac{b^2 - a^2}{ac}$.

If both roots of the quadratic $ax^2 + bx + c = 0$ lie in $(0, 2)$ then $25ac + 20bc + 16c^2$ is always

a and b are roots of the equation $2x^2 - 35x + 2 = 0$. Find the value of $(2a - 35)^3(2b - 35)^3$.

The equation $ x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 $ has how many real solutions?

If the parabola $y=ax^2+bx+c$ has vertex at $(4,2)$ and $\lambda\in[1,3]$, and the maximum value of product $abc$ is $\lambda$, then $\dfrac{|\lambda|}{24}$ is

The equation $\sqrt{3x^2 + x + 5} = x - 3$, where $x$ is real, has

What is the maximum height of any point on the curve $y = -x^2 + 6x - 5$ above the $x$-axis?

Consider the equation $x^2 + 2x - n = 0$, where $n \in \mathbb{N}$ and $n \in [5, 100]$. The total number of different values of $n$ so that the given equation has integral roots is

Let $f(x) = ax^2 + bx + c$, $a, b, c \in \mathbb{R}$. If $f(x)$ takes real values for real values of $x$ and non-real values for non-real values of $x$, then

The value of m for which one of the roots of $x^2 - 3x + 2m = 0$ is double of one of the roots of $x^2 - x + m = 0$ is

Let $\alpha,\beta$ be roots of $x^2-3x-\sqrt7=0$ and $\alpha^2+\frac1\beta,\beta^2+\frac1\alpha$ be roots of $x^2+px+q=0$. For $x^2+p^2qx-(11q+p)=0$, roots are

If α and β are roots of the equation ax2 + bx + c = 0, then the roots of the equation $a(2x+1)^2 - b(2x+1)(3-x) + c(3-x)^2 = 0$ are

If α and β, α and γ, α and δ are the roots of the equations $ax^2 + 2bx + c = 0$, $2bx^2 + cx + a = 0$ and $cx^2 + ax + 2b = 0$, respectively, where a, b and c are positive real numbers, then $\alpha + \alpha^2 =$

The sum of the non-real roots of $(x^2 + x - 2)(x^2 + x - 3) = 12$ is

If $a, b, c$ are three distinct positive real numbers, then the number of real roots of $ax^2 + 2b|x| - c = 0$ is

$x^2 - xy + y^2 - 4x - 4y + 16 = 0$ represents

If the sum of the roots of an equation is 2 and the sum of their cubes is 98, then find the equation.

80. The range of $a$ for which the equation $x^2 + ax - 4 = 0$ has its smaller root in the interval $(-1, 2)$ is

The number of integers n such that the equation $nx^2 + (n+1)x + (n+1) = 0$ has only rational roots, is equal to:

Quadratic Equations Questions (527)