Solve for "a" in Polynomial Function: 2x^3 - ax^2 - 12x - 7

[josephcollins]

Could someone please help me with this question, I'd be most obliged:

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

Thanks

 

[Gokul43201]

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.

 

[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).