Question

How many, and what type of solutions, does3x2−x−5=0 have?

2 irrational solutions
2 rational solutions
1 rational solution
2 non-real solutions

Answer 1

2 irrational solutions

Explanation:

using the quadratic formula:

`\frac{ -b \:± \sqrt{b {}^(2) - 4ac } }{2a}`

3x²−x−5=0

where a = 3, b = -1 and c = -5, plug in those values in the quadratic formula

`\frac{ - ( - 1)±\sqrt{(1) {}^(2) - 4(3)( - 5) } }{2(3)}`

you get two solutions:

`(1 + √(61) )/(6) \: and \: (1 - √(61) )/(6)`

both can be written as:

`(1± √(61) )/(6)`

They are irrational as they cannot be written in the form p/q where p and q are whole numbers (integers)