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 t are integers, and the fractions are in simplest form.
x = r − si/t,x = r + si/t

Answer 1

Explanation:

5x² − 8x + 5 = 0

delta = b²- 4ac a =5 and b = - 8 and c=5

delta = (-8)²- 4(5)(5) = 64 - 100 = -36 = (6i)² . i² = -1

x1 = (8-6i)/10 =(4-3i)/5

x2 = (8+6i)/10 =(4+3i)/5

so r=4 and s=3 and t= 5

Answer 2

Explanation:

a = 5; b = -8; c = 5

b² -4ac = (-8)² - 4 * 5 * 5 = 64 - 100 = (-36) < 0

x = -b ± √(4ac - b²) i / 2a

= - (-8) ±√ 4 * 5 * 5 - (-8)² i / 2 *5

= 8 ± √36 i

10

= 8 ± 6 i

10

= 2 (4 ± 3i) = 4 ± 3i

10 5

= 4 ± 3i

5 5

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