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

Answer:

2 irrational solutions

Step-by-step 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:

$\frac{1 + \sqrt{61} }{6} \: and \: \frac{1 - \sqrt{61} }{6}$

both can be written as:

$\frac{1± \sqrt{61} }{6}$

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