Question

Find k and the roots if

3x^2+kx+4=0 and the sum of the roots is 3

Answer 1

• k = -9
• roots: (9±√33)/6

Explanation:

In the form ...

ax^2 +bx +c = 0

the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...

-k/3 = 3

k = -9

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The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.

x^2 -3x +4/3 = 0

(x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2

(x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square

x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify