Question

Solve r²-8r-22=0

a) r=11,−2
b) r=9,−4
c) r=−11,2
d) r=−9,4

Answer 1

The solutions of the quadratic equation r²-8r-22=0 are r = 4 + √38 and r = 4 - √38.

Step-by-step explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = -8, and c = -22. Its solutions are given by the quadratic formula:

r = (-b ± √(b² - 4ac)) / 2a

Substituting the values, we have:

r = (-(-8) ± √((-8)² - 4(1)(-22))) / 2(1)

r = (8 ± √(64 + 88)) / 2

r = (8 ± √152) / 2

r = (8 ± 2√38) / 2

r = 4 ± √38

Therefore, the solutions are r = 4 + √38 and r = 4 - √38.