Question

What value does "g" have to have in order for this to be a no solution equation?

4x−9−12x+1=4(gx+5)

a) 2
b) -2
c) 4
d) -4

Answer 1

The expression is a quadratic equation and cannot have no solutions for any value of g.

Step-by-step explanation:

This expression is a quadratic equation of the form ax² + bx + c = 0, where the constants are a = 4, b = -12, and c = -9 - 1 - 20. Its solutions are given by the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

To have no solutions, the discriminant (b² - 4ac) must be negative. Let's substitute the values: (-12)² - 4(4)(-30) = 144 + 480 = 624. Since 624 is a positive number, the equation will have two solutions. Therefore, there is no value of g that will make this equation have no solutions.