List of top Mathematics Questions on Nature of Roots

The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is
The value of m for which the quadratic equation $3x^2 - 7x + m = 0$ has real and equal roots, is
The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, is
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is
The value of k for which the equation $kx^2 - 6x - 4 = 0$ has real and equal roots, is
Verify that roots of the quadratic equation (p – q)x\(^2\) + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is
Verify that roots of the quadratic equation (p – q)x\(^2\) + (q – r)x + (r – p) = 0 are equal when q + r = 2p.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is
Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).
If the quadratic equation \(9x^2 + 8kx + 16 = 0\) has real and equal roots, then the value of k is
If the roots of the quadratic equation $\sqrt{3}x^2 - kx + 2\sqrt{3} = 0$ are real and equal, then the value(s) of k is/are :
The roots of the quadratic equation \(x^2 + 9 = 0\) are
Is it possible to design a rectangular park of perimeter 80 m and area 400 \(m^2\) ? If so, find its length and breadth.
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 \(m^2\)? If so, find its length and breadth.

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 
(i) \(2x^2 + kx + 3 = 0\) (ii) \(kx (x – 2) + 6 = 0\)

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
 (i) \(2x^2 – 3x + 5 = 0\) (ii) \(3x^2 – 4\sqrt3 x + 4 = 0\)  (iii) \(2x^2 – 6x + 3 = 0\)