Question

What are the roots of 12x = 9 + 5x2?
A. `(-6 stackrel(+)(-) isqrt(3))/(10)`
B. `(-6 stackrel(+)(-) isqrt(3))/(5)`
C. `(6 stackrel(+)(-) 3i)/(5)`
D. `(-6 stackrel(+)(-) 3i)/(5)`

Answer 1

Answer:

Step-by-step explanation:

Minus 12x both sides

0=5x^2-12x+9

use quadratic formula

for 0=ax^2+bx+c

x= \frac{-b+/- \sqrt{b^2-4ac} }{2a}

given

5x^2-12x+9

a=5

b=-12

c=9

remember: i=√-1

x= \frac{-(-12)+/- \sqrt{(-12)^2-4(5)(9)} }{2(5)}

x= \frac{12+/- \sqrt{144-180} }{10}

x= \frac{12+/- \sqrt{-36} }{10}

x= \frac{12+/- (\sqrt{-1})(\sqrt{36}) }{10}

x= \frac{12+/- i(\sqrt{36}) }{10}

x= \frac{12+/- 6i }{10}

x= \frac{6+/- 3i }{5}

the roots are

x= \frac{6+ 3i }{5} and \frac{6- 3i }{5}