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GOOBER3838
17.05.2021 •
Mathematics
Question
Which of the following is equivalent to x2 – 3x – 10?
O (x - 5)(x - 2)
O (x+5)(x+2)
O (x - 5)(x + 2)
O (x+5)(x - 2)
Solved
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Ответ:
12
Step-by-step explanation:
Lets use Baskara's formula to find the roots:
[-b +- sqrt (b^2 - 4ac)]/2a =
[-b +- sqrt (b^2 - 4*4*(-27))]/8=
[-b +- sqrt (b^2 + 432)]/8=
So, we have 2 roots, lets call them x1 and x2. They are:
x1 = [-b + sqrt (b^2 + 432)]/8
x2= [-b - sqrt (b^2 + 432)]/8
Their ratio is:
x1/x2 = [[-b + sqrt (b^2 + 432)]/8] / [[-b - sqrt (b^2 + 432)]/8] = -3
The 8s disappear
[-b + sqrt (b^2 + 432)] / [-b - sqrt (b^2 + 432)] = -3
multiplying both sides by the denominator to eliminate it and solving:
[-b + sqrt (b^2 + 432)] = -3*[-b - sqrt (b^2 + 432)]
-b + sqrt (b^2 + 432) = 3b + 3sqrt (b^2 -+ 432)
Summing b in both sides to eliminate the left b
sqrt (b^2 + 432) = 4b + 3sqrt (b^2 + 432)
Subtracting sqrt (b^2 - 432) in both sides to eliminate the left term:
0 = 4b + 3sqrt (b^2 + 432) - sqrt (b^2 + 432)
0 = 4b + 2sqrt(b^2 + 432)
Dividing both sides by 2
0 = 2b + sqrt(b^2 + 432)
Subtracting 2b in both sides:
-2b = sqrt(b^2 + 432)
Squaring both sides and solving
4b^2 = b^2 + 432
3b^2 = 432
b^2 = 144
b = 12
Ready!