How do I get this answer? -3 2/3?

Question

What is the sum of the solutions of the equation 3x(squared) + 11x + 4?

Answer 1

3x^2 + 11x + 4 = 0
using quadratic formula
a = 3, b = 11, c = 4
x = (-11 +- sqrt(121 - (4*3*4)))/(2*3)
x = (-11 +- sqrt(121 - 48))/6
x = (-11 +- sqrt(73))/6
x = (-11 +- 8.54)/6
x = -3.26 or -0.41

sum of solution = -3.26 - 0.41 = -3.67 = -3 2/3

Answer 2

Sum of the Roots of a Quadratic Equation

If ax^2 + bx + c = 0,
then the sum of the roots is equal to -b / a.

If 3x^2 +11x + 4 =0,
then the sum of the roots is equal to -11 / 3 or -3 2/3.

Answer 3

3X(squared) + 11X + 4 = 3 XX + 11 X + 4
= 18 + (X-1) X

Answer 4

There is a quick way to answer this question without deriving the zeros:

In any qudratirc, ax^2 + bx + c,

1) the sum of the roots = -b/a

and

2) the product of the roots = c/a.

So, your answer would be -(11/3).

This method can be expanded to other polynomials besides quadratics. For instance:

for the quartic ax^4 + bx^3 + cx^2 + dx +e,

1) the sum of the roots = -b/a

and

2) the product of the roots = e/a.

In a cubic (or any 'odd' power polynomial) the product will be the negative ratio of the leading coefficient to the constant.

Answer 5

its possible if you have 3x^2+11x-4
3x^2+12x-x-4
(3x-1)(x+4)
x=1/3 or x = -4 (your solution)
sum of solutions
-4+(1/3)
-11/3 its the same as writing -3*(2/3)

Answer 6

the sum of the roots is eqaul to the - b term dived by the a term

in other words

sum= -11/3

formula's work wayy easier thean doing it all out if you know them :O)

so in the future just so you know the product=c/a

Answer 7

Let x1 and x2 be the two roots.
3x^2+11x+4 = 3(x-x1)(x-x2) = 3x^2-3(x1+x2)x+3x1x2
Compare the coefficients of x,
11 = -3(x1+x2)
x1+x2 = -11/3 = -3 2/3

Answer 8

-11/3

Answer 9

this is clearly a quadratic equation.

the equation to retrieve the solution is provided on this website:http://id.mind.net/~zona/mmts/miscellaneousMath/quadraticRealSolver/quadraticRealSolver.html

since it is complex to type it out here i would suggest you visit this link.

by plugging in the values based on the equation the correct answer is close to -3 2/3

Answer 10

Use the quadratic formula or divide everything by 3 and try factoring. The quadratic would be easier, I think.