what is the value of the discriminant, $b^{2}-4ac$, for the quadratic equation $0 = - 2x^{2}-3x + 8$, and…

what is the value of the discriminant, $b^{2}-4ac$, for the quadratic equation $0 = - 2x^{2}-3x + 8$, and what does it mean about the number of real solutions the equation has?\nthe discriminant is -55, so the equation has 2 real solutions.\nthe discriminant is -55, so the equation has no real solutions.\nthe discriminant is 73, so the equation has 2 real solutions.\nthe discriminant is 73, so the equation has no real solutions.

what is the value of the discriminant, $b^{2}-4ac$, for the quadratic equation $0 = - 2x^{2}-3x + 8$, and what does it mean about the number of real solutions the equation has?\nthe discriminant is -55, so the equation has 2 real solutions.\nthe discriminant is -55, so the equation has no real solutions.\nthe discriminant is 73, so the equation has 2 real solutions.\nthe discriminant is 73, so the equation has no real solutions.

Answer

Explanation:

Step1: Identificar coeficientes

Para la ecuación $0 = - 2x^{2}-3x + 8$, tenemos $a=-2$, $b = - 3$ y $c = 8$.

Step2: Calcular discriminante

Usamos la fórmula $\Delta=b^{2}-4ac$. Sustituyendo valores: $\Delta=(-3)^{2}-4\times(-2)\times8$. $\Delta = 9+64$. $\Delta=73$.

Step3: Interpretar discriminante

Como $\Delta = 73>0$, la ecuación tiene 2 soluciones reales.

Answer:

The discriminant is 73, so the equation has 2 real solutions.