English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Write the condition to be satisfied for which equations ax² + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.

Write the set of value of k for which the quadratic equations has 2x² + kx − 8 = 0 has real roots.

Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].

If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.

If the equation x² + 4x + k = 0 has real and distinct roots, then

If the equation x² − ax + 1 = 0 has two distinct roots, then

If the equation 9x² + 6kx + 4 = 0 has equal roots, then the roots are both equal to

If ax² + bx + c = 0 has equal roots, then c =

If the equation ax² + 2x + a = 0 has two distinct roots, if 

The positive value of k for which the equation x² + kx + 64 = 0 and x² − 8x + k = 0 will both have real roots, is

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q =

If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then

If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then

If the equation x² − bx + 1 = 0 does not possess real roots, then