List of top Mathematics Questions on Quadratic Equations asked in VITEEE

The roots of
\[ (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0 \] where \(a\in \mathbb{R}\) are always

Let \(f(x)=x^2+ax+b\), where \(a,b\in \mathbb{R}\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f'(x)+f''(x)=0\) are

The number of real roots of the equation \(x^4+\sqrt{x^4+20}=22\) is

In a triangle ABC, the sides \(b\) and \(c\) are the roots of the equation \(x^2-61x+820=0\) and \(A=\tan^{-1}\left(\frac{4}{3}\right)\), then \(a^2\) is equal to

If \( b^2 \geq 4ac \) for the equation \( ax^4 + bx^2 + c = 0 \), then all the roots of the equation will be real if

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if

If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is

If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the value of \( \alpha^3 + \beta^3 \) is: