If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of the quadrilateral, find the area of the quadrilateral ABCD.
Find all zeroes of the polynomial (2x4 - 9x3 + 5x2 + 3x-1) if two of its zeroes are ( 2 + √3 ) and ( 2 - √3 ).
It is given that ( 2 + √3 ) and ( 2 - √3 ) are two zeros of 2x4 - 9x3 + 5x2 + 3x-1
Let us now divide f(x) by x2-4x + 1
therefore, we have,
f(x) = (x2- 4x + 1)(2x2-x-1)
Hence, other two zeros of f(x) are the zeros of the polynomial 2x2-x-1
We have,
2x2-x-1 = 2x2- 2x+ x-1
= 2x (x-1) + 1(x-1)
= (2x+ 1)(x-1)
Hence, the other two zeros are - 1/2 and 1.
Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.
A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.