(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

Show that the locus of the centres of all circles passing through two given points A and B, is the perpendicular bisector of the line segment AB.

ΔPBC and ΔQBC are two isosceles triangles on the same base BC but on the opposite sides of line BC. Show that PQ bisects BC at right angles.

ΔPBC, ΔQBC and ΔRBC are three isosceles triangles on the same base BC. Show that P, Q and R are collinear.

In Fig. AB = AC, BD and CE are the bisectors of ∠ABC and ∠ACB respectively such that BD and CE intersect each other at O. AO produced meets BC at F. Prove that AF is the right bisector of BC.

Given: ∠BAC, a line intersects the arms of ∠BAC in P and Q. How will you locate a point on line segment PQ, which is equidistant from AB and AC? Does such a point always exist?

The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect in P. Show that P is equidistant from the opposite sides AB and CD.

By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x² + 5x – 3.

Show that (x – 2) is a factor of 3x² – x – 10 Hence factorise 3x² – x – 10.

Show that (x – 1) is a factor of x³ – 5x² – x + 5 Hence factorise x³ – 5x² – x + 5.

Show that (x – 3) is a factor of x³ – 7x² + 15x – 9. Hence factorise x³ – 7x² + 15 x – 9

Show that (2x + 1) is a factor of 4x³ + 12x² + 11 x + 3 .Hence factorise 4x³ + 12x² + 11x + 3.

Show that 2x + 7 is a factor of 2x³ + 5x² – 11x – 14. Hence factorise the given expression completely, using the factor theorem. 

Use factor theorem to factorise the following polynominals completely.

x³ + 2x² – 5x – 6

Use factor theorem to factorise the following polynominals completely. x³ – 13x – 12.

Using the Remainder and Factor Theorem, factorise the following polynomial: x³ + 10x² – 37x + 26.

If (2x + 1) is a factor of 6x³ + 5x² + ax – 2 find the value of a.

If (3x – 2) is a factor of 3x³ – kx² + 21x – 10, find the value of k.

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x² – Kx + 6 = 0. Also, find the other root of the equation.

What number should be subtracted from 2x³ – 5x² + 5x so that the resulting polynomial has 2x – 3 as a factor?

Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x³ + ax² + bx – 12.