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suter [353]
3 years ago
10

TIMED QUESTION Which are the roots of the quadratic function f(b) = b2 – 75? Select TWO options.

Mathematics
2 answers:
Vesna [10]3 years ago
7 0

The roots of the quadratic function are

a. b = 5√3

b. b = -5√3

<h3>Further explanation</h3>

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

<h2>D = b² - 4 a c</h2>

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

An axis of symmetry of quadratic equation y = ax² + bx + c is :

\large {\boxed {x = \frac{-b}{2a} } }

Let us now tackle the problem!

<u>Given:</u>

f(b) = b^2 - 75

<em>The roots of the quadratic function could be calculated when</em> f(b) = 0 :

0 = b^2 - 75

b^2 = 75

b = \pm \sqrt{75}

b = \pm \sqrt{25 \times 3}

b = \pm \sqrt{25} \times \sqrt{3}

b = \pm 5 \times \sqrt{3}

b = \pm 5\sqrt{3}

b = 5\sqrt{3} \texttt{ or } b = -5\sqrt{3}

\texttt{ }

<h3>Learn more</h3>
  • Solving Quadratic Equations by Factoring : brainly.com/question/12182022
  • Determine the Discriminant : brainly.com/question/4600943
  • Formula of Quadratic Equations : brainly.com/question/3776858

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

Setler [38]3 years ago
6 0

Answer:

b=5\sqrt{3} (b = 5 StartRoot 3 EndRoot)

and

b=-5\sqrt{3} (b = Negative 5 StartRoot 3 EndRoot)

Step-by-step explanation:

we have

f(b)=b^{2}-75

we know that

The roots of the quadratic function are the values of x when the value of the function is equal to zero

so

For f(b)=0

b^{2}-75=0

Solve for b

Adds 75 both sides

b^{2}=75

take square root both sides

b=(+/-)\sqrt{75}

Simplify

b=(+/-)5\sqrt{3}

therefore

b=5\sqrt{3} (b = 5 StartRoot 3 EndRoot)

and

b=-5\sqrt{3} (b = Negative 5 StartRoot 3 EndRoot)

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