Using division of polynomials state whether `x+6\ i s\ fa c tor\ of\ x^2-x-42` `4x-1\ i s\ a\ fa c tor\ of\ 4x^2-13 x-12` `2y-5\ i s\ fa c tor\ of\ 4y^4-10 y^3 10^2+30 y-15` `3y^2+5\ i s\ fa c tor\ of\ 6y^5+15^4+16^3+4y^2+10 y-35`

Using division show that 3y^2+5 is factor of 6y^5+15 y^4+16 y^3+4y^2+10 y-35.

Using division show that 3y^(2)+5 is factor of 6y^(5)+15y^(4)+16y^(3)+4y^(2)+10y-35

The length of common chord of the circles x^2 + y^2 - 6x - 4y + 13 - c^2 = 0 and x^2 + y^2 -4x - 6y + 13 -c^2 = 0 is

If a = 3x - 5y, b = 6x + 3y and c = 2y - 4x . Find : (i) a + b - c , (ii) 2a - 3b + 4c .

Prove that the area of the parallelogram formed by the lines 3x-4y+a=0,\ 3x-4y+3a=0,\ 4x-3y-a=0\ a n d \4x-3y-2a =0\ i s (2a^2)/7s qdotu n i t sdot

Find the value of x and y,if (x+2y)+i(2x-3y) is the conjugate of 5+4i .

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

I 3x^(2) + 4x + 1 = 0" "II. Y^(2) + 5y + 6 = 0

Find x and y if (x^4+2x i)-(3x^2+y i)=(3-5i)+(1+2y i)