Question

Calculate the discriminant to determine the number of real roots.

y = x2 – 6x + 9.

How many real roots does the equation have?
(Points : 5)
one real root
two real roots
no real roots
no solution to the equation

Answer 1

Discriminant: b² - 4ac
Discriminant: (-6)² - 4(1)(9)
Discriminant: 36 - 36
Discriminant: 0

The equation has one real root.

Answer 2

The given equation is $y = x^2 - 6x + 9.$Therefore, The equation has one real root.

How to use the discriminant to find the property of solutions of given quadratic equation?

Let the quadratic equation given be of the form $ax^2 + bx + c = 0$, then

The quantity b^2 - 4ac is called its discriminant.

The solution contains the term $\sqrt{b^2 - 4ac}$

which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative.

The given equation is

$y = x^2 - 6x + 9.$

Discriminant: b² - 4ac

Discriminant: (-6)² - 4(1)(9)

Discriminant: 36 - 36

= 0

Therefore, The equation has one real root.

Learn more about the discriminant of a quadratic equation here:

https://brainly.com/question/18659539

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