Question

One root of `x^3^2 + ax-6 = 0` is 3,. What is the value of `a` and the other roots?

Answer 1

`a = -7.` The other two roots are`-1 and -2`.

Explanation:

Let the other two roots be p and q.

Sum of the roots

= 3 + p + q = - the coefficient of `x^2` = 0. So, p + q = -3.

Sum of the products, taken two at a time

= 3( p + q) + pq = 3(-3)+ pq = the coefficient of x = a. So, pq = a + 9.

The product of all the roots

= 3pq = - the constant term = 6. So, pq = 2. And so, `a = -7`..

Now, `p-q = +-sqrt ((p+q)^2-4pq)=+-sqrt(9-8)=+-1.`

So, (p, q) = (-1, -2) and also (-2, -1).

Anyway, the other two roots are `-1 and -2`..