If α and β are the roots of the quadratic equation 17x²+43x−73 = 0 , construct a quadratic equation whose roots are α + 2 and β + 2.

If α and β are the roots of the quadratic equation 2x²−7x+13 = 0 , construct a quadratic equation whose roots are α² and β².

If the sides of a cubic box are increased by 1, 2, 3 units respectively to form a cuboid, then the volume is increased by 52 cubic units. Find the volume of the cuboid.

If α, β and γ are the roots of the cubic equation x³+2x²+3x+4 = 0, form a cubic equation whose roots are, 2α, 2β, 2γ

Find the sum of squares of roots of the equation 2x⁴- 8x³+ 6x²-3 = 0.

Solve the equation 9x³- 36x²+ 44x -16 = 0 if the roots form an arithmetic progression.

Solve the equation 3x³-26x²+52x - 24 = 0 if its roots form a geometric progression.

Solve the equation
2x³ - 9x² + 10x = 3

Solve the equation x³- 5x²- 4x + 20 = 0

Find the roots of 2x³ + 3x² + 2x + 3 = 0