Finite Math Examples

x^{2} + 3 x + 2 = 0

$x^{2} + 3 x + 2 = 0$

Step 1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b^{2} - 4 (a c)

$b^{2} - 4 (a c)$

Step 2

Substitute in the values of

a

$a$ ,

b

$b$ , and

c

$c$ .

3^{2} - 4 (1 \cdot 2)

$3^{2} - 4 (1 \cdot 2)$

Step 3

Evaluate the result to find the discriminant.

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Step 3.1

Simplify each term.

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Step 3.1.1

Raise

3

$3$ to the power of

2

$2$ .

9 - 4 (1 \cdot 2)

$9 - 4 (1 \cdot 2)$

Step 3.1.2

Multiply

- 4 (1 \cdot 2)

$- 4 (1 \cdot 2)$ .

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Step 3.1.2.1

Multiply

2

$2$ by

1

$1$ .

9 - 4 \cdot 2

$9 - 4 \cdot 2$

Step 3.1.2.2

Multiply

- 4

$- 4$ by

2

$2$ .

9 - 8

$9 - 8$

9 - 8

$9 - 8$

9 - 8

$9 - 8$

Step 3.2

Subtract

8

$8$ from

9

$9$ .

1

$1$

1

$1$

Step 4

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant

(Δ)

$(Δ)$ :

Δ > 0

$Δ > 0$ means there are

2

$2$ distinct real roots.

Δ = 0

$Δ = 0$ means there are

2

$2$ equal real roots, or

1

$1$ distinct real root.

Δ < 0

$Δ < 0$ means there are no real roots, but

2

$2$ complex roots.

Since the discriminant is greater than

0

$0$ , there are two real roots.

Two Real Roots