Question

Solve 3x^2 +11x+6=0 Answers -2/3,-3 2/3,3 0

Answer 1

Answer: First Option

$x_1=-\frac{2}{3}$ and  $x_2=-3$

Step-by-step explanation:

We have the following quadratic equation:

$3x^2 +11x+6=0$

To solve this equation use the quadratic formula

For an equation of the form:

$ax ^ 2 + bx + c = 0$

The quadratic formula is:

$x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$

Note that in this case: $a=3,\ b=11,\ c=6$

Then:

$x=\frac{-11\±\sqrt{11^2-4(3)(6)}}{2(3)}$

$x=\frac{-11\±\sqrt{121-72}}{6}$

$x=\frac{-11\±\sqrt{49}}{6}$

$x=\frac{-11\±7}{6}$

$x_1=\frac{-11+7}{6}$

$x_1=-\frac{2}{3}$

$x_2=\frac{-11-7}{6}$

$x_2=\frac{-18}{6}$

$x_2=-3$

The solutions are: $x_1=-\frac{2}{3}$ and  $x_2=-3$

Answer 2

Answer:

-$\frac{2}{3}$,-3

Step-by-step explanation:

Given equation,

$3x^2+11x+6=0$

By the middle term splitting,

$3x^2 + (9+2)x + 6 = 0$

$3x^2 + 9x + 2x + 6 = 0$

$3x(x+3)+2(x+3)=0$

$(3x+2)(x+3)=0$

By zero product product,

3x + 2 = 0 or x + 3 = 0

x = $-\frac{2}{3}$ or x = -3

which is the solution of the given equation.

Hence, FIRST option is correct.