which are the roots of the quadratic function f(b) = b² - 75? select two options.\nb = 5√3\nb = -5√3\nb =…
which are the roots of the quadratic function f(b) = b² - 75? select two options.\nb = 5√3\nb = -5√3\nb = 3√5\nb = -3√5\nb = 25√3
Answer
Explanation:
Step1: Set the function equal to zero
Set $b^{2}-75 = 0$.
Step2: Isolate $b^{2}$
Add 75 to both sides: $b^{2}=75$.
Step3: Solve for $b$
Take the square - root of both sides. Remember, when $x^{2}=a$ ($a\geq0$), $x=\pm\sqrt{a}$. So $b=\pm\sqrt{75}$.
Step4: Simplify $\sqrt{75}$
We know that $75 = 25\times3$, so $\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}$. Then $b = 5\sqrt{3}$ or $b=-5\sqrt{3}$.
Answer:
A. $b = 5\sqrt{3}$ B. $b=-5\sqrt{3}$