English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Prove that the points A(1, 7), B (4, 2), C(−1, −1) 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) = x^2 + 7x + 12` and verify the relation between its zeroes and coefficients.

Find the zeroes of the polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients

Find the zeroes of the quadratic polynomial `f(x) = x^2 + 3x ˗ 10` and verify the relation between its zeroes and coefficients. 

Find the zeroes of the quadratic polynomial `f(x) = 5x^2 ˗ 4 ˗ 8x` and verify the relationship between the zeroes and coefficients of the given polynomial.

State fundamental theorem of arithmetic?

One zero of the polynomial `3x^3+16x^2 +15x-18 is 2/3` . Find the other zeros of the  polynomial.

If f(x) =`x^3-3x+5x-3` is divided by g(x)=`x^2-2` 

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 `(x^4 + 4x^3 – 2x^2 – 20x – 15)` if two of its zeroes are `sqrt5 and –sqrt5.` 

Find all the zeroes of polynomial `(2x^4 – 11x^3 + 7x^2 + 13x – 7)`, it being given that two of its zeroes are `(3 + sqrt2) and (3 – sqrt2)`. 

If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` , write the other zero. 

Find the zeroes of the polynomial `x^2 + x – p(p + 1) `