Solve using the quadratic formula.
a) x^2 - 7x + 12 = 0
a = 1 b = -7
x = -b +/- the sr of b^2 - 4ac /2a
7 +/- the sr of -7^2 - 4(1)(12) /2a
7 +/- the sr of -49 - 48 /2a
7 +/- the sr of -97 /2a
7 +/- 97 /2a
-90/2=-45
-104/2= 54
The roots are -45 and 54.
did i solve this correctly?
x^2 - 7x + 12 = 0
The 12 can factor into -3 and -4 to add to -7 in the middle term.
(x-3)(x-4) = 0
x = 3 or 4.
Well, you were on the right track, but your calculations went a bit astray. Let's go through it step by step:
For the quadratic equation x^2 - 7x + 12 = 0, we have a = 1, b = -7, and c = 12.
Using the quadratic formula, we have:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(-7) +/- sqrt((-7)^2 - 4(1)(12))) / (2*1)
x = (7 +/- sqrt(49 - 48)) / 2
x = (7 +/- sqrt(1)) / 2
x = (7 +/- 1) / 2
So the two possible solutions are:
x = (7 + 1) / 2 = 8 / 2 = 4
x = (7 - 1) / 2 = 6 / 2 = 3
Therefore, the correct roots are x = 4 and x = 3. Keep up the good work and keep clowning around with math!
No, your solution is incorrect. Let's go through the quadratic formula step-by-step to find the correct solutions.
Given: x^2 - 7x + 12 = 0
Step 1: Identify the values of a, b, and c in the quadratic equation.
In this case, a = 1, b = -7, and c = 12.
Step 2: Apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values:
x = (-(-7) ± √((-7)^2 - 4(1)(12))) / (2(1))
x = (7 ± √(49 - 48)) / 2
x = (7 ± √1) / 2
x = (7 ± 1) / 2
Step 3: Simplify the expression:
x = (7 + 1) / 2 or x = (7 - 1) / 2
x = 8 / 2 or x = 6 / 2
x = 4 or x = 3
So, the correct solutions for the equation x^2 - 7x + 12 = 0 are x = 4 and x = 3.
Yes, you solved it correctly. The quadratic equation given is x^2 - 7x + 12 = 0, and you correctly identified a = 1 and b = -7. Then applying the quadratic formula, you correctly calculated:
x = (-(-7) +/- sqrt((-7)^2 - 4(1)(12))) / (2 * 1)
Simplifying further:
x = (7 +/- sqrt(49 - 48)) / 2
x = (7 +/- sqrt(1)) / 2
Now, taking the square root of 1 simplifies to:
x = (7 +/- 1) / 2
Which gives us two possibilities:
x = (7 + 1) / 2 = 8 / 2 = 4
x = (7 - 1) / 2 = 6 / 2 = 3
So the roots of the quadratic equation are x = 4 and x = 3. Therefore, your solutions of -45 and 54 appear to be incorrect.