How many, and what type of solutions, does3x2−x−5=0 have?
1 answer:
Answer:
2 irrational solutions
Step-by-step explanation:
using the quadratic formula:
![\frac{ -b \:± \sqrt{b {}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-b%20%5C%3A%C2%B1%20%5Csqrt%7Bb%20%7B%7D%5E%7B2%7D%20-%204ac%20%7D%20%20%20%7D%7B2a%7D%20)
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)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%20%28%20-%201%29%C2%B1%5Csqrt%7B%281%29%20%7B%7D%5E%7B2%7D%20-%204%283%29%28%20-%205%29%20%7D%20%7D%7B2%283%29%7D%20)
you get two solutions:
![\frac{1 + \sqrt{61} }{6} \: and \: \frac{1 - \sqrt{61} }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%20%2B%20%20%5Csqrt%7B61%7D%20%7D%7B6%7D%20%5C%3A%20%20and%20%5C%3A%20%20%5Cfrac%7B1%20-%20%20%5Csqrt%7B61%7D%20%7D%7B6%7D%20)
both can be written as:
![\frac{1± \sqrt{61} }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%C2%B1%20%5Csqrt%7B61%7D%20%7D%7B6%7D%20)
They are irrational as they cannot be written in the form p/q where p and q are whole numbers (integers)
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Hope I Helped You!!! :-)
Have A Good Day!!!
Answer:
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Step-by-step explanation: