English Medium कक्षा १० - CBSE Question Bank Solutions

Find the values of k for which the roots are real and equal in each of the following equation:

\[4 x^2 + px + 3 = 0\]

Find the values of k for which the quadratic equation 

\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.

Find the values of p for which the quadratic equation 

If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.

If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\]  has equal roots, find the value of k.

If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.

Find the value of p for which the quadratic equation 

\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.

Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.

If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.

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