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Hatshy [7]
3 years ago
5

Determine the factors of x2 − 7x − 10. (5 points) a (x + 2)(x − 5) b Prime c (x − 2)(x + 5) d (x + 10)(x − 1)

Mathematics
1 answer:
Savatey [412]3 years ago
6 0

For this case we must factor the following expression:

x ^ 2-7x-10

To factor, we must find two numbers that when added together give -7 and when multiplied by -10.

It is observed that there are not two whole numbers that comply with the aforementioned.

Thus, the following equation applies:

x = \frac {-b \pm\sqrt{b ^ 2-4 (a) (c)}} {2 (a)}

Where:

a = 1\\b = -7\\c = -10

We replace:

x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 10)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 40}} {2}\\x = \frac {7 \sqrt {89}} {2}

So, the roots are:

x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}

Answer:

x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}

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D + q = 40
.10d +.25q= $7.75

d +q = 40
d =40-q
.10(40-q) +.25q= $7.75
4 - .10q + .25q =7.75
4 +.15q =7.75
4-4 +.15q =7.75-4
.15q= 3.75
.15q/.15 = 3.75/.15
q = 25

d =40-25
d = 15

Check
.10(15) +.25(25)= $7.75
1.5+6.25=7.75
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