Question

Solve the following quadratic equation using the quadratic formula.

5x^2– 8x+ 5 = 0
Write the solutions in the following form, where r, s, and tare integers, and the fractions are in simplest form.
R+ si/t, x=r+si/t

Answer 1

answer in picture

Explanation:

Answer 2

Either

x = 4+3i /5 or x = 4-3i /5

Explanation:

To solve the quadratic equation using the quadratic formula, we will follow the steps below;

write down the quadratic formula;

x = -b±√b² - 4ac /2a

First lets compare the equation 5x² - 8x + 5 = 0 to the standard quadratic equation ax² + bx + c

a = 5 b = -8 and c= 5

we can now proceed to substitute the above value into the quadratic formula and then solve. That is;

x = -b±√b² - 4ac /2a

= -(-8)±√(-8)² - 4(5)(5) /2(5)

= 8 ±√64-100 /10

=8 ±√-36 /10

= 8 ±√36 . √-1 /10 note that √-1 = i

=8±6i /10

=
`(8)/(10)` ±
`(6 i)/(10)`

=
`(4)/(5)` ±
`(3i)/(5)`

Either

x = 4+3i /5 or x = 4-3i /5