Question

Find all real and non-real roots of the function ƒ(x) = x2 + 49. Question 1 options: A) x = –7, 7 B) x = –7i, 7i C) x = –49i, 49i D) x = i + 7, i – 7

Answer 1

Given:

The function is:

$f(x)=x^2+49$

To find:

The all the real and non-real roots of the given function.

Solution:

We have,

$f(x)=x^2+49$

For roots, $f(x)=0$,

$x^2+49=0$

$x^2=-49$

Taking square root on both sides, we get

$x=\pm \sqrt{-49}$

$x=\pm \sqrt{-1}\sqrt{49}$

$x=\pm 7i$                $[\because \sqrt{-1}=i]$

The roots of the given function are -7i and 7i.

Therefore, the correct option is B.