Finite Math Examples

$16 x^{2} + 25 = 40 x$

Step 1

Subtract $40 x$ from both sides of the equation.

$16 x^{2} + 25 - 40 x = 0$

Step 2

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

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

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 40)}^{2} - 4 (16 \cdot 25)$

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Raise $- 40$ to the power of $2$ .

$1600 - 4 (16 \cdot 25)$

Step 4.1.2

Multiply $- 4 (16 \cdot 25)$ .

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Step 4.1.2.1

Multiply $16$ by $25$ .

$1600 - 4 \cdot 400$

Step 4.1.2.2

Multiply $- 4$ by $400$ .

$1600 - 1600$

Step 4.2

Subtract $1600$ from $1600$ .

$0$

Step 5

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant $(Δ)$ :

$Δ > 0$ means there are $2$ distinct real roots.

$Δ = 0$ means there are $2$ equal real roots, or $1$ distinct real root.

$Δ < 0$ means there are no real roots, but $2$ complex roots.

Since the discriminant is equal to $0$ , there are two equal roots, or one distinct real root.

One Real Root