Question

How to find the value of the discriminant of F? How many distinct real numbers zeroes does F have?f(x) = -4x2 + 10x – 8

Answer 1

f(x)=-4x2+10x-8

The expression is in the form:

ax^2+bx+c

In this case:

a=-4

b=10

c=-8

Apply the quadratic formula:

$x=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a}$

Replace the values:

$x=\frac{-10\pm\sqrt[\square]{10^2-4(-4)-8}}{2(-4)}$

The discriminant part is the part of the quadratic formula underneath the square root.

Discriminant : 10^2-(4 (-4)-8)

To find if it has zeroes solve the discriminant:

10^2-(4 (-4)-8) = 100-128 = -28

Since the discriminant is negative, it has no real number solutions.