If 3 times the square of an integer is added to 1 times the integer, the result is 2. Find the integers.
Equation:
3x^2 + 1*x = 2
I don't think that equation will factor, so you're going to have to use the quadratic formula to find what x is.
3x^2 + x - 2 = 0
I got x to be -1 and 2/3
Let me know if you got the same from applying the quadratic formula
To solve this problem, let's first set up an equation based on the given information.
Let's assume the integer is represented by the variable 'x'. According to the given information, "3 times the square of an integer is added to 1 times the integer, the result is 2."
This can be written as:
3x^2 + 1x = 2
Now, we can solve this quadratic equation to find the value(s) of 'x'.
Rearranging the equation:
3x^2 + x - 2 = 0
To solve for 'x', we can either factorize the quadratic equation or use the quadratic formula.
Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for 'x' are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 3, b = 1, and c = -2.
Substituting these values into the quadratic formula:
x = (-(1) ± √((1)^2 - 4(3)(-2)) / (2(3))
x = (-1 ± √(1 + 24)) / 6
x = (-1 ± √25) / 6
Now, we have two possible solutions:
x = (-1 + 5) / 6 = 4/6 = 2/3
x = (-1 - 5) / 6 = -6/6 = -1
So, the two possible integers are 2/3 and -1.