How do you find the value of the discriminant and determine the nature of the roots $-9b^2=-8b+8$ ?

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Answer 1 · 2017-08-22T12:40:05

See a solution process below:

First, convert the equation to standard form:

$-9b^2 + color(red)(8b) - color(blue)(8) = -8b + 8 + color(red)(8b) - color(blue)(8)$

$-9b^2 + 8b - 8 = 0$

For $ax^2 + bx + c = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-b +- sqrt(b^2 - 4ac))/(2a)$

The discriminate is the portion of the quadratic equation within the radical: $color(blue)(b)^2 - 4color(red)(a)color(green)(c)$

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

$color(red)(-9)$ for $color(red)(a)$

$color(blue)(8)$ for $color(blue)(b)$

$color(green)(-8)$ for $color(green)(c)$

$color(blue)(8)^2 - (4 * color(red)(-9) * color(green)(-8))$

$64 - 288$

$-224$

Because the discriminate is negative there will be a complex solution.

How do you find the value of the discriminant and determine the nature of the roots -9b^2=-8b+8-9b^2=-8b+8?