SOLVING CUBIC EQUATIONS WITH GIVEN ROOTS WORKSHEET

Problem 1 :

Solve the equation

3x³ - 16x² + 23x - 6 =0

if the product of two roots is 1.

Solution

Problem 2 :

Find the sum of the square of roots of the equation

2x⁴ - 8x³ + 6x² - 3 = 0

Solution

Problem 3 :

Solve the equation 

x³ - 9x² + 14x + 24 = 0

if it is given that two of its roots are in the ratio 3 : 2

Solution

Problem 4 :

If  α, β and γ are the roots of the polynomial equation

ax³ + bx² + cx + d = 0

find the value of Σα/βγ in terms of the coefficients.

Solution

Problem 5 :

If  α, β, γ and δ are the roots of the polynomial equation

2x⁴ + 5x³ - 7x² + 8 = 0

find a quadratic equation with integer coefficients whose roots are α + β + γ + δ and α β γ δ.

Solution