What is 3/4(x2+4x+6)=13x-2

Mathematics

1 answer:

maxonik [38]3 years ago

6 0

Answer:

$x_1=12.65\\\\x_2=0.685$

Step-by-step explanation:

$\frac{3}{4}(x^2+4x+6)=(13x-2)\\\\Multiply\ both\ sides\ by\ 4.\\\\3(x^2+4x+6)=4(13x-2)\\\\3x^2+12x+18=52x-8\\\\3x^2+12x+18-(52x-8)=0\\\\3x^2+12x-52x+18+8=0\\\\3x^2-40x+26=0$

Roots of Polynomial:

$Roots\ are\ polynomial\ ax^2+bx+c=0\\\\x=\frac{-b\pm \sqrt{(b^2-4ac)}}{2a}$

$Here\ a=3,\ b-40,\ c=26\\\\x=\frac{-(-40)\pm \sqrt{(-40)^2-4\times 3\times 26}}{2\times 3}\\\\x=\frac{40\pm\sqrt{1288}}{6}\\\\x_1=\frac{40+\sqrt{1288}}{6}\approx 12.65\\\\x_2=\frac{40-\sqrt{1288}}{6}\approx 0.685$

You might be interested in

Find the length of the radius of the circle whose perimeter is xcm and the area is

Jobisdone [24]

$\bf \stackrel{\textit{perimeter}}{\textit{circumference}}\textit{ of a circle}\\\\ C = 2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=x \end{cases}\implies x = 2\pi r\implies \boxed{\cfrac{x}{2\pi }=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=x \end{cases}\implies x = \pi \left( \boxed{\cfrac{x}{2\pi }} \right)^2\implies x = \pi \cdot \cfrac{x^2}{2^2\pi^2}$

$\bf x = \cfrac{x^2}{4\pi }\implies 4\pi x = x^2\implies \cfrac{4\pi x}{x}=x\implies \blacktriangleright 4\pi = x\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since the radius is}}{r = \cfrac{x}{2\pi }}\implies r =\cfrac{4\pi }{2\pi }\implies \blacktriangleright r = 2\blacktriangleleft$