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

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

Explanation:

Given

`x = (-(-6) \± √((-6)^2 - 4(1)(10)))/(2*1)`

Required

Solve, in terms of i

We have:

`x = (-(-6) \± √((-6)^2 - 4(1)(10)))/(2*1)`

Solve the expressions in bracket

`x = (-(-6) \± √(36 - 40))/(2*1)`

`x = (-(-6) \± √(-4))/(2)`

Express -4 as 4 * -1

`x = (-(-6) \± √(-4*1))/(2)`

Split

`x = (-(-6) \± √(4)*√(-1))/(2)`

In complex numbers;

`i = \sqrt{-1`

So, we have:

`x = (-(-6) \± 2*i)/(2)`

`x = (6 \± 2i)/(2)`

Factorize

`x = (2(3 \± i))/(2)`

`x = 3 \± i`

Split

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