maths question (1 Viewer)

[19KANguy]

1. Find the cubic equation whose roots are twice those of the equation 3x^3 - 2x^2 + 1 = 0
2. Find two values of m such that the roots of the equation x^3 + 2x^2 + mx - 16 = 0 are a, b, ab. Use these values of m to find a and b

 

[pikachu975]

1) let x = the roots (a, b, c) of 3x^3 - 2x^2 + 1 = 0
let y = 2a, 2b, 2c (roots of the new cubic equation)
y = 2x
x = y/2

Now sub x = y/2 into the cubic
3(y/2)^3 - 2(y/2)^2 + 1 = 0
3y^3 / 8 - y^2 / 2 + 1 = 0
3y^3 - 4y^2 + 8 = 0

Sub x back in
3x^3 - 4x^2 + 8 = 0

 

[19KANguy]

thx