Question

What is the discriminant of 3x^2 + 2x +1 = 0?

Answer 1

-8

Explanation:

The formula for solving for the discriminant is b^2-4ac.

3x^2 + 2x +1 = 0

a= 3

b= 2

c= 1

Plug these values into the corresponding variable.

2^2-4(3)(1)

= 4-12

=-8

Answer 2

Discriminant: b² - 4ac = - 8 (no real solutions)

Explanation:

We are given the following quadratic equation, 3x² + 2x + 1 = 0, where a = 3, b = 2, and c = 1.

In the Quadratic Formula,
`\displaystyle\mathsf{x\:=\:(-b\pm√(b^2-4ac))/(2a)}`, the expression under the radical symbol, "b² - 4ac" is the discriminant, which tells us the number of solutions of a given quadratic equation. When we substitute the values for a, b, and c of a given quadratic equation into the quadratic formula, we are essentially solving for its number of solutions.

Discriminant: b² - 4ac

• If b² - 4ac > 0, then it means that the quadratic equation has two real solutions.

• If b² - 4ac = 0, then it means that the quadratic equation has one real solution.

• If b² - 4ac < 0, then it means that the quadratic equation has no real solutions.

Solution:

Given the quadratic equation, 3x² + 2x + 1 = 0, where a = 3, b = 2, and c = 1, let us substitute the values for a, b, and c into the discriminant to determine its number of solutions:

Discriminant: b² - 4ac = (2)² - 4(3)( 1 ) = 4 - 12 = - 8

Hence, the discriminant of 3x² + 2x + 1 = 0 is -8, which means that the given quadratic equation has no real solutions. This implies that the 3x² + 2x + 1 = 0 has no x-intercepts (because the graph does not cross the x-axis).

Attached is a screenshot of the graphed quadratic equation, 3x² + 2x + 1 = 0, where it shows that it does not cross the x-axis, proving that there are no real solutions.