Question

what is the value of the discriminant of the quadratic equation -1 = 5x² - 2x, and what does its value mean about the number of real number solutions the equation has? the discriminant is equal to -16, which means the equation has no real number solutions. the discriminant is equal to -16, which means the equation has two real number solutions. the discriminant is equal to 24, which means the equation has no real number solutions. the discriminant is equal to 24, which means the equation has two real number solutions.

Explanation:

Step1: Rewrite equation in standard form

$5x^{2}-2x + 1=0$

Step2: Identify coefficients

$a = 5$, $b=-2$, $c = 1$

Step3: Calculate discriminant

$\Delta=b^{2}-4ac=(-2)^{2}-4\times5\times1=4 - 20=-16$

Step4: Determine number of solutions

Since $\Delta<0$, no real - number solutions.

Answer:

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