what is the value of the discriminant of the quadratic equation -1 = 5x² - 2x, and what does its value mean…

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $- 1=5x^{2}-2x$ as $5x^{2}-2x + 1=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 5$, $b=-2$, $c = 1$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a = 5$, $b=-2$, $c = 1$ into it: $\Delta=(-2)^{2}-4\times5\times1=4 - 20=-16$.

Step3: Determine the number of real - solutions

If $\Delta>0$, the quadratic equation has two distinct real solutions; if $\Delta = 0$, the quadratic equation has one real solution; if $\Delta<0$, the quadratic equation has no real solutions. Since $\Delta=-16<0$, the equation has no real solutions.

Answer:

The discriminant is equal to -16, which means the equation has no real number solutions.