Quadratic Equations and Inequalities · Mathematics · NDA

If $\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0 + a_1 x + a_2 x^2 + a_3 x^3 + x^4 = 0$ where $a_0, a_1, a_2, a_3$ are integers, then which...

If $a$, $b$, and $c$ $(a > 0, c > 0)$ are in GP, then consider the following in respect of the equation $ax^2 + bx + c = 0$: 1. The equation has ima...

If $x^2 + mx + n$ is an integer for all integral values of $x$, then which of the following is/are correct?1. $m$ must be an integer2. $n$ must be an ...

Under which one of the following conditions does the equation $\left(\cos \beta-1\right)x^2+(\cos \beta)x+\sin \beta=0$ in $x$ have a real root for $\...

If $\rm {k}=\frac{{c}}{2},({c} \neq 0)$, then the roots of the equation are :

If k = c, then the roots of the equation are:

For how many integral values of k, the equation x2 - 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ?&nb...

How many real numbers satisfy the equation |x - 4| + |x - 7| = 15 ?

α and β are distinct real roots of the quadratic equation x2 + ax + b = 0. Which of the following statements is/are sufficient to find α ?&n...

What is the HM of the roots of the equation ? 

What is the GM of the roots of the equation ?

For how many quadratic equations, the sum of roots is equal to the product of roots?

Let p, q(p > q) be the roots of the quadratic equation x2 + bx + c = 0 where c > 0. If p2 + q2 − 11pq = 0, then what is p − q equ...

Let α and β be the roots of the equation x2 + px + q = 0. If α3 and β3 are the roots of the equation x2 + mx + n = 0, then what is the value of m...

Let α and β be the roots of the equation x2 - ax - bx + ab - c = 0. What is the quadratic equation whose roots are a and b?

If the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?

Let α and β (α > β) be the roots of the equation x2 - 8x + q = 0. If α2 - β2 = 16, then what is the value of q?...