Determine the Nature of the Roots Using the Discriminant 6t^2-7t=0

$6 t^{2} - 7 t = 0$

Step 1

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

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

Step 2

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

${(- 7)}^{2} - 4 (6 \cdot 0)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$49 - 4 (6 \cdot 0)$

Multiply $- 4 (6 \cdot 0)$ .

Multiply $6$ by $0$ .

$49 - 4 \cdot 0$

Multiply $- 4$ by $0$ .

$49 + 0$

Add $49$ and $0$ .

$49$

Step 4

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

$Δ > 0$ 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 greater than $0$ , there are two real roots.

Two Real Roots