Question

What is the value of the discriminant of the quadratic equation −1 = 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?

The discriminant is equal to −16, which means the equation has no real number solutions.
The discriminant is equal to −16, which means the equation has two real number solutions.
The discriminant is equal to 24, which means the equation has no real number solutions.
The discriminant is equal to 24, which means the equation has two real number solutions.

Answer 1

For the equation:
-1=5 x^2 - 2 x
5 x^2 - 2 x + 1 = 0,           then we substitute: a=5,  b=-2,  c =1
to discriminant formula: D= b^2 - 4 a c = (-2)^2 - 4 * 5 * 1 = 4 - 20 = - 16
Answer:
The discriminant is equal to -16 which means the equation has no real number solutions. 

Answer 2

The correct option regarding the discriminant of the quadratic equation is given by:

The discriminant is equal to −16, which means the equation has no real number solutions.

What is the discriminant of a quadratic equation and how does it influence the solutions?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

• If $\mathbf{\Delta > 0}$, and it is a perfect square, it has 2 rational solutions.

• If $\mathbf{\Delta > 0}$, and it is not a perfect square, it has 2 irrational solutions.

• If $\mathbf{\Delta = 0}$, it has 1 rational solutions.

• If $\mathbf{\Delta < 0}$, it has 2 complex solutions.

In this problem, we have that:

5x² - 2x = -1

5x² - 2x + 1 = 0

Hence the coefficients are a = 5, b = -2 and c = 1, while the discriminant is given by:

$\Delta = b^2 - 4ac = (-2)^2 - 4(5)(1) = -16$

No real solutions, hence the first option is correct.

More can be learned about the discriminant of quadratic equations at https://brainly.com/question/19776811

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