Algebra Examples

x^{2} - 11 = 0

$x^{2} - 11 = 0$

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

$c$ .

0^{2} - 4 (1 \cdot - 11)

$0^{2} - 4 (1 \cdot - 11)$

Step 3

Evaluate the result to find the discriminant.

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Simplify each term.

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Raising

0

$0$ to any positive power yields

0

$0$ .

0 - 4 (1 \cdot - 11)

$0 - 4 (1 \cdot - 11)$

Multiply

- 4 (1 \cdot - 11)

$- 4 (1 \cdot - 11)$ .

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Multiply

- 11

$- 11$ by

1

$1$ .

0 - 4 \cdot - 11

$0 - 4 \cdot - 11$

Multiply

- 4

$- 4$ by

- 11

$- 11$ .

0 + 44

$0 + 44$

0 + 44

$0 + 44$

0 + 44

$0 + 44$

Add

0

$0$ and

44

$44$ .

44

$44$

44

$44$

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

x^{2} - 11 = 0

$x^{2} - 11 = 0$

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