Question

Which are the roots of the quadratic function f(b) = b ^ 2 - 75 Select two options .

Answer 1

Quadratic function: Let $x$ be a variable, then a quadratic function is of the form

$\quad\quad f(x)=ax^{2}+bx+c$

where $a,\:b,\:c\in\mathbb{R}$ with $a\neq 0$

Solution:

The given quadratic function is

$\quad\quad f(b)=b^{2}-75$

To find the roots of this function, we equate $f(b)$ with zero $(0)$

$\Rightarrow f(b)=0$

$\Rightarrow b^{2}-75=0$

$\Rightarrow b^{2}=75$

$\Rightarrow b^{2}=3\times 25$

$\Rightarrow b^{2}=(\sqrt{3})^{2}\times 5^{2}$

$\Rightarrow b^{2}=(5\sqrt{3})^{2}$

$\Rightarrow b=\pm 5\sqrt{3}$

Answer: Therefore the roots of the given quadratic function are

$\quad\quad\quad b=\pm 5\sqrt{3}$.