Determine the discriminant for the quadratic equation -3=x^2+4x+1. Based on the discriminant value, how many real number solutions does the equation have ? Discriminant value = b^2-4ac

One real root (multiplicity 2).

Step-by-step explanation:

-3=x^2+4x+1

x^2 + 4x + 4 = 0

Discriminant = 4^2 - 4*1*4 = 0

There is one real root (multiplicity 2).

The equation has 1 real solution.

The quadratic function is given as:

Add 3 to both sides of the equation

This gives

Rewrite the equation as:

A quadratic equation is represented as:

By comparison, we have:

The discriminant (d) is calculated as:

So, we have:

Evaluate like terms

Given that the discriminant value is 0, it means that the equation has 1 real solution.

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x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

step-by-step explanation:

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