How do you find the value of the discriminant and determine the nature of the roots $4a^2=8a-4$ ?

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Answer 1 · 2018-04-02T10:16:21

See a solution process below:

First, put this equation in standard quadratic form:

$4a^2 = 8a - 4$

$4a^2 - color(red)(8a) + color(blue)(4) = 8a - color(red)(8a) - 4 + color(blue)(4)$

$4a^2 - 8a + 4 = 0 - 0$

$4a^2 - 8a + 4 = 0$

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:

$color(red)(4)$ for $color(red)(a)$

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

$color(green)(4)$ for $color(green)(c)$

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

$64 - 64 =>$

$0$

Because the discriminate is $0$ there will be just one solution or one root.

How do you find the value of the discriminant and determine the nature of the roots 4a^2=8a-44a^2=8a-4?