Question

If m is a variable and n is a constant, and 6m^2 +5m=n, then which of the following values for n would result in an equation with no real solutions?

a) n=6/5
b) n=1
c) n=-5/6
d) n=-6/5

Answer 1

Upon calculating the discriminant for the quadratic equation template ax^2 + bx + c = 0, we conclude that n = -6/5 is the only given value that would result in an equation with no real solutions.

Step-by-step explanation:

To determine which value of n would result in an equation with no real solutions for 6m^2 + 5m = n, we can analyze the quadratic equation in the form ax^2 + bx + c = 0. For a quadratic equation to have no real solutions, the discriminant b^2 - 4ac must be negative. Applying this concept to the given equation, we have a = 6, b = 5, and c = -n. Thus, the discriminant would be 5^2 - 4(6)(-n) = 25 + 24n. For the discriminant to be negative, n must be less than -25/24. Therefore, we compare the given values of n to find the one that is less than -25/24.

• n = 6/5 is greater than -25/24, so it would not result in no real solutions.
• n = 1 is greater than -25/24, so it would not result in no real solutions.
• n = -5/6 is greater than -25/24, so it would not result in no real solutions.
• n = -6/5 is less than -25/24, so this value would result in no real solutions.

Therefore, the correct answer is d) n = -6/5.