Question

how many real - number solutions does the equation have? 4x² - 3x = - 2

Explanation:

Step1: Rewrite to standard quadratic form

$4x^2 - 3x + 2 = 0$

Step2: Identify coefficients a,b,c

$a=4,\ b=-3,\ c=2$

Step3: Calculate discriminant $\Delta=b^2-4ac$

$\Delta=(-3)^2 - 4\times4\times2 = 9 - 32 = -23$

Step4: Analyze discriminant sign

Since $\Delta=-23<0$, no real roots exist.

Answer:

none