Question

3x^2+2x+5=0 Quadratic equation

Answer 1

Step-by-step explanation:

use formula

(-b+√b2-4ac)/2a

a=3, b=2 , c=5

(-2+√4-4×3×5)/2×3

(-2+√-56)/6

(-2+2√-14)/6

(-2 +2√14i)/6

Answer 2

The quadratic equation has a form of

$ax^2+bx+c=0\wedge a\neq0$

We have

$3x^2+2x+5=0$

Hence our coefficients are

$a=3,b=2,c=5$

Now to find a solution we have to look at the equation, since equation has no apparent solution given by the factorisation we are forced to use quadratic formula.

$x_{1,2}=-\dfrac{b^2\pm\sqrt{b^2-4ac}}{2a}$

Put in the data and simplify a bit

$x_{1,2}=-\dfrac{2^2\pm\sqrt{2^2-4\cdot3\cdot5}}{2\cdot3} \\x_{1,2}=-\dfrac{4\pm\sqrt{-56}}{6}\in\mathbb{C}$

And we get two complex solutions

$x_1=\boxed{-\dfrac{4}{6}-\dfrac{56}{6}i} \\x_2=\boxed{-\dfrac{4}{6}+\dfrac{56}{6}i}$

Hope this helps.

r3t40