Find the value of n if both sum and product of roots of the quadratic equation mx² - 5x + n = 0 are equal to 10?
Answer: 5
Explanation
Given the quadratic equation mx² - 5x + n = 0:
Sum of roots = -(-5/m) = 5/m
Product of roots = n/m
Given both sum and product of roots are equal to 10:
5/m = 10 => m = 1/2
n/m = 10 => n = 10m
n = 10 * (1/2)
n = 5
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