Question

Determine the type and number of solutions of 4x^2-5x+1=0.

A. Two real solutions
B. One real solution
C. Two imaginary solutions

Answer 1

4x² - 5x + 1 = 0
a = 4; b = - 5, c = 1
Δ = b² - 4.a.c
Δ = (-5)² - 4.4.1
Δ = 25 - 16
Δ = 9

x = - b ± √Δ / 2.a

`x = (-5\± √(9) )/(2*4)`

`x = (-5\±3)/(8)`

`x' = (-5-3)/(8) = (-8)/(8) = -1`

`x' = (-5+3)/(8) = (-2)/(8) (/2) = (-1)/(4)`


A. Two real solutions (x' = -1 and x'' = -1/4)