1) Find two numbers whose difference and whose quotient are each equal to 5?

2) Find the number of negative roots of the equation (x^4) + (x^2) + 1 = 0?

Solution

1) 5/4 and 25/4

Explanation: Since the quotient is 5 the difference is four times the smaller number. Hence the numbers are 5/4 and 25/4.

2. None

Explanation: If x is negative then x^4 and x^2 are both positive and so the LHS of the given equation is positive, and hence there is no negative root for the given equation.