# Polynomial Functions

1. Jun 19, 2004

### josephcollins

Q) Find the value of "a" for which the function
2x^3 - ax^2 - 12x - 7
has a repeated factor.

Thanks

2. Jun 19, 2004

### Gokul43201

Staff Emeritus
If you mean two identical roots, then ...

write $$2x^3 - ax^2 - 12x - 7 = (x-b)^2(2x-c)$$

Expand the RHS and compare coefficients. You have 3 equations in 3 unknowns.

3. Jul 4, 2004

### robert Ihnot

Since we are seeking only a specific solution, we can keep in mind that if the cubic has a double root, that this root is also present in its derative. The derative is: 2(3X^2-aX-6). Here if we let a =3, we get X =2, -1. -1 works in the original equation and the factoring then is 2(x+l)^2(x-7/2).

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