English Medium Class 10 - CBSE Question Bank Solutions

A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

If x² (a² + b²) + 2x (ac + bd) + c² +d² = 0 has no real roots, then:

If the one root of the equation 4x² – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:

Find the sum of the roots of the equation x² –  8x + 2 = 0

If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.

Which of the following equations has the sum of its roots as 3?

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

Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?

Which of the following equations has two distinct real roots?

(x² + 1)² – x² = 0 has ______.

State whether the following quadratic equation have two distinct real roots. Justify your answer.

x² – 3x + 4 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

2x² + x – 1 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

`2x^2 - 6x + 9/2 = 0`

State whether the following quadratic equation have two distinct real roots. Justify your answer.

3x² – 4x + 1 = 0

State whether the following quadratic equation have two distinct real roots. Justify your answer.

(x + 4)² – 8x = 0

Every quadratic equation has exactly one root.

Every quadratic equation has at least one real root.

A quadratic equation with integral coefficient has integral roots. Justify your answer.

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.