3n2+5n-100=?
3n^2+5n-100=?
If this is a quadratic equation, the your ? is 0
If you are dealing with the corresponding quadratic function you would normally find it as
y = 3n^2 + 5n - 100 , where y is the dependent variable, and n is the independent variable
What about it ?
well, 3n^2+5n-100 = (3n+20)(n-5)
To solve the expression 3n^2 + 5n - 100, we can use the quadratic formula or factorization methods.
Method 1: Using the quadratic formula
The quadratic formula is given by:
n = (-b ± √(b^2 - 4ac)) / (2a)
In the given expression, a = 3, b = 5, and c = -100. Substituting these values into the quadratic formula, we get:
n = (-5 ± √(5^2 - 4*3*(-100))) / (2*3)
Simplifying further:
n = (-5 ± √(25 + 1200)) / 6
n = (-5 ± √(1225)) / 6
n = (-5 ± 35) / 6
Therefore, we have two possible solutions:
n = (-5 + 35) / 6 = 30/6 = 5
n = (-5 - 35) / 6 = -40/6 = -20/3
So, the solutions for the expression 3n^2 + 5n - 100 are n = 5 and n = -20/3.
Method 2: Factorization
To solve the expression using factorization, we need to find two numbers whose product is ac (-100 in this case) and whose sum is b (5 in this case). After factoring, we can rewrite the expression as:
3n^2 + 5n - 100 = (3n - 20)(n + 5)
So, the solutions are the values of n that make each factor equal to zero:
3n - 20 = 0 → n = 20/3
n + 5 = 0 → n = -5
Therefore, the solutions for the expression 3n^2 + 5n - 100 are n = 20/3 and n = -5.