Question

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

Answer 1

Answer:

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).

Answer 2

The equation has 1 real solution.

The quadratic function is given as:

$-3=x^2+4x+1$

Add 3 to both sides of the equation

$3-3=x^2+4x+1 + 3$

This gives

$0=x^2+4x+4$

Rewrite the equation as:

$x^2+4x+4 = 0$

A quadratic equation is represented as:

$ax^2+bx+c = 0$

By comparison, we have:

$a =1$

$b =4$

$c = 4$

The discriminant (d) is calculated as:

$d =b^2 - 4ac$

So, we have:

$d =4^2 - 4 \times 1 \times 4$

$d =16 - 16$

Evaluate like terms

$d = 0$

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

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