Posted by **Connor** on Tuesday, August 31, 2010 at 7:29pm.

Determine K and solve the equation x^3-kx^2+3x+54=0, if one of its zeros is triple of another.

- Pre Calc -
**Reiny**, Tuesday, August 31, 2010 at 8:15pm
let the roots be a, 3a and b

then

(x-a)(x-3a)(x-b) = x^3 - kx^2 + 3x + 54

looking at the last term -3a^2b = 54

a^2b = -18 , the only square factors of -18 are 1 and 9

case 1: a=1, b = -18

then

(x-1)(x-3)(x+18) would be the expression

this give us x^3 + 14x^2 - 69x + 54

which would not match up the x terms

case 2: a=3, b=-2

then

(x-3)(x-9)(x+2) would be the expression for

x^3 - 10x^2 + 3x + 54

this matches if k = 10

and the roots are 3,9 and -2

(there should be an easier way to do this)

## Answer this Question

## Related Questions

- Pre Clac - Determine k and solve the equation: x^3-kx^2+3x+54=0, if one of it ...
- pre calc - Determine between which consecutive integers one or more real zeros ...
- Pre Calc - 7x^3-24x^2-19x+12 -----------------=f(x) 2x^3-4x^2-40x+80 -Determine ...
- Pre calc - How do you write a quadratic equation in standard form for a given ...
- Pre Calc (For Reiny) - Thanks so much your method worked perfectly! My solution ...
- Pre-calc - Use the given zero to find the remaining zeros of the function: h(x)=...
- Pre-Cal. - Determine between which consecutive integers one or more real zeros ...
- Pre-Calc - Can you show me how to find the rectangular equation of r=2costheta...
- Math - Find the Zeros of the following functions f(x) = x/3 +5 ^ That one is ...
- pre-calc - how do i solve this equation algebraicly solve the equation 1+25cos(x...