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16.11.2020 •
Mathematics
Given the following ogive, what does the 5th point (22, 77) tell you about the data? PHOTO INCLUDED
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Ответ:
a) The discriminant of the equation = - 44
b)The nature of the roots will be imaginary.
c)![x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}](/tpl/images/0355/9625/1559e.png)
Step-by-step explanation:
Here, the given expression is![15x^{2} = 4x -1](/tpl/images/0355/9625/95d58.png)
or,![15x^{2} - 4x + 1 = 0](/tpl/images/0355/9625/3c164.png)
Now the discriminant (D) of a quadratic equation![ax^{2} +b x + c = 0](/tpl/images/0355/9625/5a3b8.png)
D =![b^{2} - 4ac = (-4)^{2} - 4(15) (1) = 16 - (60) = -44](/tpl/images/0355/9625/1f9a3.png)
Hence, the discriminant of the equation = - 44
As D< 0, so the roots will be imaginary.
Now,by quadratic formula :![x = \frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}](/tpl/images/0355/9625/d1353.png)
So, here![x = \frac{-(-4) \pm \sqrt{D} }{2a} = \frac{4 \pm \sqrt{(-44 )} }{30}](/tpl/images/0355/9625/087ec.png)
So, either![x = \frac{4 + \sqrt{(-44 )} }{30} or, x = \frac{4 - \sqrt{(-44 )} }{30}](/tpl/images/0355/9625/51ea8.png)
or,![x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}](/tpl/images/0355/9625/1559e.png)