I need help solving this:
6x^2-x-12=0
I usually could do this yet i have completely forgotten what i need to do seeing as there is a number infront of the x^2
This equation is of the general form
a x^2 + bx + c = 0
The solution is always
x = [-b +/- sqrt (b^2 - 4ac)]/(2a)
= [1 +/- sqrt (1 + 288)]/12
= [1 +/- 17)/12
= 3/2 or -4/3
The equation could also have been factored into
(2x - 3)(3x + 4) = 0
14.
a)Write the prime factorization of 3600 using exponets
b)write the prime factorization of the square root of 3600
98
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a) To find the prime factorization of 3600, we need to express it as a product of its prime factors.
Step 1: Start by dividing 3600 by the smallest prime number, which is 2. Since 3600 is an even number, it is divisible by 2. Hence, we have:
3600 ÷ 2 = 1800
Step 2: Continue dividing the resultant quotient by 2 until we can no longer divide evenly:
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 2 = 225
Step 3: Now, we move on to the next prime number, which is 3.
225 ÷ 3 = 75
75 ÷ 3 = 25
Step 4: Next, we check if 25 is divisible by 3. Since it is not, we move on to the next prime number, which is 5.
25 ÷ 5 = 5
Step 5: Finally, we check if 5 is divisible by any prime numbers greater than 5, but it is not.
Since we have reached a prime number (5) and cannot divide any further, we have found the prime factorization of 3600:
3600 = 2^4 * 3^2 * 5^2
b) To find the prime factorization of the square root of 3600, we start by finding the prime factorization of 3600 using the steps in part a):
3600 = 2^4 * 3^2 * 5^2
Now, we can find the square root of each prime factor:
√(2^4) = 2^2 = 4
√(3^2) = 3
√(5^2) = 5
Therefore, the prime factorization of the square root of 3600 is:
√3600 = 4 * 3 * 5
= 60