Question

Lin decides to solve the equation using the quadratic formula. Here is her work: xxx=−b±b2−4ac−−−−−−−√2a=−(−6)±(−6)2−4(1)(10)−−−−−−−−−−−−−√2(1)=6±36−40−−−−−−√2 Lin knows 36−40 is a negative number and isn't sure what to do next. Show how Lin can write her solution using i.

Answer 1

Answer:

$x = 3 + i\ or\ x = 3 - i$

Step-by-step explanation:

Given

$x = \frac{-(-6) \± \sqrt{(-6)^2 - 4(1)(10)}}{2*1}$

Required

Solve, in terms of i

We have:

$x = \frac{-(-6) \± \sqrt{(-6)^2 - 4(1)(10)}}{2*1}$

Solve the expressions in bracket

$x = \frac{-(-6) \± \sqrt{36 - 40}}{2*1}$

$x = \frac{-(-6) \± \sqrt{-4}}{2}$

Express -4 as 4 * -1

$x = \frac{-(-6) \± \sqrt{-4*1}}{2}$

Split

$x = \frac{-(-6) \± \sqrt{4}*\sqrt{-1}}{2}$

In complex numbers;

$i = \sqrt{-1$

So, we have:

$x = \frac{-(-6) \± 2*i}{2}$

$x = \frac{6 \± 2i}{2}$

Factorize

$x = \frac{2(3 \± i)}{2}$

$x = 3 \± i$

Split

$x = 3 + i\ or\ x = 3 - i$