Based on the value of the discriminant, how many real solutions does 12z² + 5z + 4 = 0 have?

The quadratic equation 12 z 2 + 5 z + 4 = 0 has no real solutions because the discriminant is − 167 , which is less than zero. Therefore, the solutions are complex numbers. Hence, there are two complex solutions to the equation.
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Answered by Anonymous | 2025-07-04

To determine the number of real solutions for the quadratic equation 12 z 2 + 5 z + 4 = 0 , we need to evaluate its discriminant.
The discriminant D of a quadratic equation in the form a x 2 + b x + c = 0 is given by:
D = b 2 − 4 a c
In this equation, the coefficients are:

a = 12
b = 5
c = 4

Now, substitute these values into the discriminant formula:
D = ( 5 ) 2 − 4 × 12 × 4 D = 25 − 192 D = − 167
The value of the discriminant D = − 167 is less than zero. This tells us that the quadratic equation has no real solutions but instead has two complex (or imaginary) solutions.
In summary, for the equation 12 z 2 + 5 z + 4 = 0 , based on the discriminant, there are no real solutions . Instead, there are two complex solutions.

Answered by BenjaminOwenLewis | 2025-07-06