If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m.
Answer Details
Let's first recall the formula for the sum of the roots of a quadratic equation in the form ax\(^2\) + bx + c = 0:
Sum of roots = -b/a
In the given equation, 2x\(^2\) + 5mx + n = 0, the coefficient of x\(^2\) is 2, which means a = 2. Therefore, the sum of the roots can be expressed as:
Sum of roots = - (5m) / 2
We are given that the sum of the roots is 5, so we can set up an equation:
5 = - (5m) / 2
Multiplying both sides by -2, we get:
-10 = 5m
Dividing both sides by 5, we obtain:
m = -2
Therefore, the value of m is -2.
So the answer is -2.0.