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harkovskaia [24]
2 years ago
8

Factor 3x^2-20x-7.

Mathematics
1 answer:
cestrela7 [59]2 years ago
3 0

Hi,

Without discriminant:

3x^2-20x-7\\\\ =3(x^2-\dfrac{2*10}{3} )-7\\\\ =3(x^2-\dfrac{2*10}{3}+\dfrac{100}{9} )-\dfrac{100}{3}-7\\\\ =3(x-\dfrac{10}{3})^2-\dfrac{121}{3}\\\\ =\sqrt{3}[(x-\dfrac{10}{3})+\dfrac{11}{3}]*\sqrt{3}[(x-\dfrac{10}{3})-\dfrac{11}{3}]\\\\ =3(x+\frac{1}{3})(x-\dfrac{21}{3})\\\\ =(3x+1)(x-7)

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The sample space for the event of rolling two dice is presented below

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(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

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Therefore:

P(rolling a 5 or a 6)  =\dfrac{20}{36}

The probability distribution of this event is given as follows.

\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|

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