Pace Edu.

If A + B = 45 Prove that (cotA - 1)(cotB - 1) = 2

Solve 3x² + 11x + 10 = 0

If A + B = 45, Prove that (1 + tanA) (1 + tanB) = 2

If points A(4, 3) and B(x, 5) are on circle with centre O(2, 3), find the value x

Find values of x for which distance between points P(4, -5) and Q(12, x) is 10 units

Divide 3x⁵ - 4x⁴ + 3x³ + 2x by x² - 3 using synthetic method

Find remainder when x³ - 2x² - 8x - 1 is divided by x +1

By actual division find the quotient and remainder when x⁴ + 1 is divided by x-1

Find Remainder p(x) = 2x² - 7x² + 9x - 13, g(x) = x - 3

Find remainder p(x) = 3x⁴ - 6x² - 8x - 2, g(x) = x - 2

Find quotient and remainder p(x) = x³ - 6x² + 9x + 3 , g(x) = x - 1

Find remainder and quotient of 6x³ + 13x² + 3 divide by 3x + 2

If p(x) = x³ - 5x² + 4x - 3 and g(x) = x - 2, show that p(x) is not a multiple of factor g(x)

Find quotient and remainder of 2x³ - 9x² + x +15 dividing by 2x - 3

If p(x) = 2x³ - 11x² - 4x + 5 and g(x) = 2x + 1 show that g(x) is not a factor of p(x)

Polynomials (2x³ + x² - ax +2) and (2x³-3x²-3x+a) when divided by (x-2) leave same remainder. Find a

If Polynomials 2x³+ ax² +3x -5 and x³ + x² - 2x + a leave same remainder when divided by x-2, Find a

If p(x) = x³ - x + 1 and g(x) = 2 - 3x. check whether p(x) is a multiple of g(x)

Show that 2x - 3 is a factor of 2x³ - 9x² + x + 12

If (x - a) is a factor of (x³ - ax² + 2x + a - 1) then find the value of a

Find value of a for which (x - 4) is a factor of (2x³ - 3x² - 18x + a)

Find value of a for which (x + 1) is a factor of (ax³ + x² - 2x + 4a - 9)

Show that p - 1 is a factor of p^10 - 1 and also p^11 - 1

Find value of k for which (x - 1) is a factor of (2x³ - 9x² + x + k)

If (x + 2a) is a factor of x⁵ - 4a²x³ + 2x + 2a + 3, Find a

Find value of m so that 2x - 1 is a factor of 8x⁴ - 4x³ − 16x² - 10x + m

Find value of a for which polynomial (x⁴ - x³ - 11x² - x + a) is divisible by (x + 3)

If x³ + ax² + bx + 6 has x-2 as a factor and leaves a remainder 3 when divided by x-3. find a and b

Show that x - 1 is a factor of 2x⁴ + 9x³ + 6x² -11x - 6

Show that (x - 3) is a factor of 2x³ + 7x² - 24x - 45

Show that (x + 2) is a factor of (x⁴ - x² - 12)

Show that x + 5 is a factor of 2x³ + 9x² - 11x - 30

Prove that 2x⁴ - 5x³ + 2x² - x + 2 is divisible by x² - 3x + 2

Show that (x³ - 3x² - 13x + 15) is exactly divisible by (x² + 2x - 3)

Find value of a and b so that polynomial x³ + 10x² + ax + b is exactly divisible by (x-1) and (x-2)

Find a and b so polynomial (x⁴ + ax³ - 7x² - 8x + b) exactly divisible by (x + 2) as well as (x+3)

Find Conjugate of (√(5 + 12i) + √(5 - 12i))/(√(5 + 12i) - √(5 - 12i))

Find x and y for which the complex numbers -3 + i x²y and x² + y + 4i are conjugates of each other

Find real values of x and y for which (x - iy)(3 + 5i) is conjugate of (-6 - 24i)

If z = 2 + i , Prove that :- z³ + 3z² - 9z + 8 = 1 + 14 i

Show that (3 + 2i)/(2 - 3i) + (3 - 2i)/(2 + 3i) is purely real

Find x and y If (x⁴ + 2xi) - (3x² + yi) = (3 - 5i) + (1 + 2yi)

Express (1 - 2i)^-3 in standard form a + ib

If x - iy = √(a - ib/c - id) Prove that (x² + y²)² = (a² + b²)/(c² + d²)

Express (2 - 3i)³ in the form (a + ib)

Prove that :- 1 + i^2 + i^4 + i^6 = 0

Find value of √(-36) * √(16)

Factorize :- x² + 11x + 30

Factorize :- x² + 18x + 32

Factorize :- x² + 20x - 69