Find the solutions of the equation 3x^2 – x – 4 = 0.
Factor it into (3x - 4)(x + 1)
Then set it equal to 0.
(3x - 4)(x + 1)=0
3x = 4
x = 4/3
x = -1
Solutions are x = 4/3, -1
This is what I thought to begin with! Thanks for the help!
To find the solutions of the equation 3x^2 – x – 4 = 0, we can use the quadratic formula.
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Comparing our equation to the standard quadratic form ax^2 + bx + c = 0, we have:
a = 3, b = -1, c = -4
Substituting these values into the quadratic formula, we get:
x = (-(-1) ± sqrt((-1)^2 - 4(3)(-4))) / (2(3))
Simplifying further:
x = (1 ± sqrt(1 + 48)) / 6
x = (1 ± sqrt(49)) / 6
x = (1 ± 7) / 6
So, the solutions of the equation 3x^2 – x – 4 = 0 are:
x = (1 + 7) / 6 = 8 / 6 = 4/3
x = (1 - 7) / 6 = -6 / 6 = -1
Therefore, the solutions of the equation 3x^2 – x – 4 = 0 are x = 4/3 and x = -1.
To find the solutions of the equation 3x^2 - x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, we have a = 3, b = -1, and c = -4. Plugging these values into the quadratic formula, we get:
x = (-( -1) ± √((-1)^2 - 4 * 3 * -4)) / (2 * 3)
Simplifying further:
x = (1 ± √(1 + 48)) / 6
x = (1 ± √49) / 6
x = (1 ± 7) / 6
This gives us two possible solutions:
x = (1 + 7) / 6 => x = 8 / 6 => x = 4/3
and
x = (1 - 7) / 6 => x = -6 / 6 => x = -1
Hence, the solutions to the equation 3x^2 - x - 4 = 0 are x = 4/3 and x = -1.