Question

Yes I’m dumb sorry but just help PLEASE

Answer 1

Answer:

Case 1:    2 solutions

Case 2:    1 solution

Case 3:    none/imaginary solutions

Step-by-step explanation:

The discriminant comes from the square root section of the quadratic formula:

$x= \frac{-b±\sqrt{b^{2}-4ac}}{2a}$    (ignore the Â, it's a formatting error)

The quadratic formula is used to find the solutions for quadratic equations. Quadratic equations are in the format ax² + bx + c. To solve for "x", you would substitute "a", "b" and "c" into the formula.

Why the discriminant works:

$\sqrt{b^{2}-4ac }$

When you have to square root a number, it has to be positive inside the root (or else you get imaginary numbers).

Example: (if the inside of the root is less than 0)

If b = 4, a = 5, c = 1 :

b² - 4ac

= 4² - 4(5)(1)

= 16 - 20

= -4

√-4 is imaginary. The quadratic equation has no solutions because you can't do the rest of the quadratic formula.

Example: (inside of the root is 0)

If b = 4, a = 4, c = 1 :

b² - 4ac

= 4² - 4(4)(1)

= 16 - 16

= 0

There will be one solution. In the quadratic formula, this affects where there is a ± sign. See the formula again.

$x= \frac{-b±\sqrt{b^{2}-4ac}}{2a}$    If the square root area equals 0:

$x= \frac{-b±0}{2a}$              Adding and subtracting 0 give the same answer.

Therefore there is only one solution.

Example: (inside of the root is greater than 0)

If b = 4, a = 3, c = 1 :

b² - 4ac

= 4² - 4(3)(1)

= 16 - 12

= 4

There will be two solutions. Notice where the ± sign is again in the uadratic formula.

$x= \frac{-b±\sqrt{b^{2}-4ac}}{2a}$  

$x= \frac{-b±\sqrt{4}}{2a}$        Substitute the answer for b² - 4ac

$x= \frac{-b±2}{2a}$           You can get two different answers between adding and subtracting 2.