Mathematics
The expression 2x3 + ax2 + bx - 2 leaves remainders 0 and 7 when divided by (x + 2) and (2x - 3), respectively. Calculate the values of a and b. Factorise the expression completely.
Related Questions
An express train makes a run of 240 km at a certain speed. Another train whose speed is 12 km/h less takes an hour longer to cover the same distance. Find the speed of the express train.
Draw and describe the locus in each of the following cases :
(i) The locus of vertices of all isosceles triangles having a common base.
(ii) The locus of points inside a circle and equidistant from two fixed points on the circle.
(iii) The locus of centres of all circles passing through two fixed points.
(iv) The locus of a point in rhombus ABCD which is equidistant from AB and AD.
A number m is randomly selected from the numbers 2, 3, 4 and then a number n is randomly selected from 1, 4, 9. What is the probability that the product of numbers m and n is less than 12?
Points (8, 0) and (-3, 0) are invariant points under reflection in the line L1, points (0, -9) and (0, 5) are invariant points under reflection in the line L2.
(i) Name or write down equations of the lines L1 and L2.
(ii) Write down the images of points P(3, 5) and Q(-8, 3) after reflection in line L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the images as P" and Q" respectively.
(iv) Describe a single transformation that maps P' to P".