Question

Determine the value of m such that the equation
x³+mx-1=0
x³-3x+m=0
have a common root
@Zarkon @zepdrix

Answer 1

Im not the best at these, but is this just asking you to solve for m in terms of x?

Answer 2

i have a different idea - but i need check it - moment please

Answer 3

I've got an answer jhonyy, but im not sure its correct. Im going off the fact that a common zero of two polynomials is a root of their difference.

Answer 4

^^possible only for quadratic equation provided coeff. of x^2 `1`

Answer 5

Okay I came up with a method. But i think I am doing some algebraic mistakes.
Start by considering x =a and then make two equations. Now come up with value of a in terms of m i.e. a = m+1/m+3
Next make a different equation by multiplying the first with 3 and second with m. And then come up with value of a^3 in terms of m . Compare the second a^3 with the first a by cubing the first a. Value of m will come

Answer 6

sorry not is right

Answer 7

my idea

Answer 8

I am pretty sure its correct

Answer 9

yes this make sens - i agree your idea Faiq

Answer 10

x = A
[1]-[2]
Am-1 +3A -m = 0
A(3+m) = m+1
A = m+1/m+3

3[1] +m[2]
3A³+3Am-3+A³m -3Am+m²=0
A³(3+m)+m²-3=0
A³= (3-m²)/3+m

A³= A³
(m+1/m+3)³ = (3-m²)/3+m
But this doesnt give me m = -2