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GaryK [48]
3 years ago
11

Which are the roots of the quadratic function f(b) = b2 – 75? Select two options. b = 5 StartRoot 3 EndRoot b = Negative 5 Start

Root 5 Endroot b = 3 StartRoot 5 Endroot b = Negative 3 StartRoot 5 EndRoot b = 25 StartRoot 5 EndRoot

Mathematics
2 answers:
yawa3891 [41]3 years ago
8 0

Answer:

b = 5 StartRoot 3 EndRoot

b = Negative 5 StartRoot 3 EndRoot

Step-by-step explanation:

we have

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

Remember that the root of a function is the value of x when the value of the function is equal to zero

In this problem

The roots are the values of b when the function f(b) is equal to zero

so

For f(b)=0

b^{2}-75=0

b^{2}=75

square root both sides

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

Simplify

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

b=5\sqrt{3}  and b=-5\sqrt{3}

therefore

b = 5 StartRoot 3 EndRoot

b = Negative 5 StartRoot 3 EndRoot

Dominik [7]3 years ago
6 0

The roots of the quadratic function are 5√3 and -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

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