Find all values of a, for which the equation has different sign roots? (one is positive and another negative) (a - 2)x^2 - 3ax + a + 5 =0?
This is a Quadratic Equation.
Have you learned the Quadratic Formula?
The radicand in the Quadratic Formula is B^2 - 4*A*C.
The expression B^2 - 4*A*C is called the Discriminant. Try looking up "Discriminant" in your textbook's index, to find out where your text talks about its uses.
One use of the Discriminant is to determine information about the solutions to a Quadratic Formula.
For example, if the value of the Discriminant is positive, then the Quadratic Equation has two distinct solutions.
Here are some hints: The equation in your exercise is written in Standard Form:
Ax^2 + Bx + C = 0
Can you identify the following expressions, from your equation?
A = ?
B = ?
C = ?
If you cannot, let us know. But, if you can see what expressions in your equation represent A,B,C, then substitute them into the Discriminant.
You will then have an expression containing the symbol a. Simplify this expression. You then need to determine the values of a that cause this expression -- the simplified Discriminant -- to be positive (i.e., write and solve an inequality greater than zero).
If you get stuck, please show us your work thus far. :cool:
