Question #4e2fa

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Question #4e2fa

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Answer 1 · 2017-10-16T13:36:01

$(y + \frac{7}{2} - \frac{\sqrt{37}}{2}) (y + \frac{7}{2} + \frac{\sqrt{37}}{2})$ $(y+7/2-sqrt37/2)(y+7/2+sqrt37/2)$

Explanation:

We will find the zeros of the trynomial by the quadratic formula
(the zeros of the generic trynomial

$a x^{2} + b x + c$ $ax^2+bx+c$

are
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+-sqrt(b^2-4ac))/(2a)$ and the trynomial will be
$a (x - x_{1}) (x - x_{2})$ $a(x-x_1)(x-x_2)$

Then our zeros are:

$y_{1, 2} = \frac{- 7 \pm \sqrt{7^{2} - 4 \cdot 3}}{2} = \frac{- 7 \pm \sqrt{37}}{2} = - \frac{7}{2} \pm \frac{\sqrt{37}}{2}$ $y_(1,2)=(-7+-sqrt(7^2-4*3))/2=(-7+-sqrt37)/2=-7/2+-sqrt37/2$

and we can factor the given trynomial as:

$(y + \frac{7}{2} - \frac{\sqrt{37}}{2}) (y + \frac{7}{2} + \frac{\sqrt{37}}{2})$ $(y+7/2-sqrt37/2)(y+7/2+sqrt37/2)$

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Question #4e2fa

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