List of top Mathematics Questions on Quadratic Equations asked in KEAM

What is the value of n when \( t_n = \frac{n(n+6)}{n+4} \) and \( t_n = 5 \)?
If \( f(x) = x^2 + 2x f'(1) + f''(2) \) for all \( x \), then \( f(0) \) is equal to:
If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=
Let $ {{z}_{1}} $ and $ {{z}_{2}} $ be the roots of the equation $ {{z}^{2}}+pz+q=0 $ where p, q are real. The points represented by $ {{z}_{1}},{{z}_{2}} $ and the origin form an equilateral triangle, if
Given $ tan\text{ }A $ and $ tan\text{ B} $ are the roots of $ {{x}^{2}}-ax+b=0 $ . The value of $ {{\sin }^{2}}(A+B) $ is
The argument of the complex number $ \left( \frac{i}{2}-\frac{2}{i} \right) $ is equal to
Suppose that two persons $A$ and $B$ solve the equation $ {{x}^{2}}+ax+b=0 $ . While solving $A$ commits a mistake in the coefficient of $ x $ was taken as $15$ in place of $-9$ and finds the roots as $ -7 $ and $ -2 $ . Then, the equation is