English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Prove that the points A(1, 7), B(4, 2), C(−1, −1), and D(−4, 4) are the vertices of a square.

An equilateral triangle has two vertices at the points (3, 4) and (−2, 3), find the coordinates of the third vertex.

Show that the quadrilateral whose vertices are (2, −1), (3, 4) (−2, 3) and (−3,−2) is a rhombus.

Find the circumcenter of the triangle whose vertices are (–2, –3), (–1, 0), (7, –6).

If the point P(x, y) is equidistant from the points A (5, 1) and B (1, 5), prove that x = y.

Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)

Two opposite vertices of a square are (–1, 2) and (3, 2). Find the coordinates of other two vertices.

If A (–1, 3), B (1, –1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Find the zeros of the polynomial f(x) = x² + 7x + 12 and verify the relation between its zeroes and coefficients.

Find the zeroes of the polynomial f(x) = x² – 2x – 8 and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial f(x) = x² + 3x – 10 and verify the relation between its zeroes and coefficients.

Find the zeroes of the quadratic polynomial f(x) = 5x² – 4 – 8x and verify the relationship between the zeroes and coefficients of the given polynomial.

One zero of the polynomial 3x³ + 16x² + 15x – 18 is `2/3`. Find the other zeros of the polynomial.

Find the quotient and the remainder when f(x) = x³ – 3x² + 5x – 3 is divided by g(x) = x² – 2.

Find all the zeroes of `(2x^4 – 3x^3 – 5x2 + 9x – 3)`, it is being given that two of its zeroes are `sqrt3 and –sqrt3`. 

Obtain all other zeroes of (x⁴ + 4x³ – 2x² – 20x – 15) if two of its zeroes are `sqrt(5)` and `-sqrt(5)`.

Find all the zeroes of polynomial (2x⁴ – 11x³ + 7x² + 13x – 7), it being given that two of its zeroes are `(3 + sqrt(2))` and `(3 - sqrt(2))`.

If one zero of the polynomial x² – 4x + 1 is `(2 + sqrt(3))`, write the other zero.

Find the zeros of the polynomial x² + x – p(p + 1).

Find the zeros of the polynomial x² – 3x – m(m + 3).