English Medium Class 10 - CBSE Important Questions

Sum of the areas of two squares is 640 m². If the difference of their perimeters is 64 m. Find the sides of the two squares.

If the quadratic equation (c² – ab) x² – 2 (a² – bc) x + b² – ac = 0 in x, has equal roots, then show that either a = 0 or a³ + b³ + c³ = 3abc ?

Solve the given quadratic equation for x : 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0 ?

Find the positive value(s) of k for which quadratic equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots ?

Solve for x :

x² + 5x − (a² + a − 6) = 0

If x = −2 is a root of the equation 3x² + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x² + k(4x + k − 1) + p = 0 are equal.

If 1 is a root of the quadratic equation 3x² + ax – 2 = 0 and the quadratic equation a(x² + 6x) – b = 0 has equal roots, find the value of b ?

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?

Solve the following quadratic equation for x:

`4sqrt3x^3+5x-2sqrt3=0`

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

Solve for x: `3x^2-2sqrt3x+2=0`

Solve the following quadratic equation for x:

x² − 4ax − b² + 4a² = 0

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

For what values of k, the roots of the equation x² + 4x +k = 0 are real? 

Find the value of k for which the roots of the equation 3x² -10x +k = 0 are reciprocal of each other.

Find the value(s) of k for which the pair of equations
kx +  2y = 3
3x + 6y = 10 has a unique solution.

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm² and 121 cm². If EF = 15⋅4 cm, find BC.

Write the discriminant of the quadratic equation (x + 5)² = 2 (5x − 3).

In the quadratic equation kx² − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.

Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is ______.