Mathematics: X² + 9x + 4 = FACTORISE

the answer is B Step-by-step explanation:...

X² + 9x + 4 = FACTORISE - id947321413, xmanavongrove55

foreverrocky12p2asun

31.01.2022

$-\frac{1}{4} (-2x-9+\sqrt{65})(2x+9+\sqrt{65})$

Step-by-step explanation:

We have a second-degree polynomial:

I will find the roots (y = 0) completing the square:

$x^2+9x+\frac{81}{4}-\frac{81}{4}+4=0$

$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +4 =0$

$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +\frac{16}{4} =0$

$\left(x+\frac{9}{2} \right)^2 -\frac{65}{4} =0$

$\left(x+\frac{9}{2} \right)^2 =\frac{65}{4}$

$\left(x+\frac{9}{2} \right)^2 =\pm \sqrt{\frac{65}{4} }$

$x =-\frac{9}{2} \pm \frac{\sqrt{65} }{2}$

$x =\frac{-9 \pm \sqrt{65} }{2}$

$\boxed{x_1 =\frac{-9 + \sqrt{65} }{2}}$

$\boxed{x_2 =\frac{-9 - \sqrt{65} }{2}}$

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