How do you find the value of the discriminant and determine the nature of the roots #4a^2=8a-4#?

Question

Eva Adamson · Accepted Answer

See a solution process below:

First, put this equation in standard quadratic form: #4a^2 = 8a - 4# #4a^2 - color(red)(8a) + color(blue)(4) = 8a - color(red)(8a) - 4 + color(blue)(4)# #4a^2 - 8a + 4 = 0 - 0# #4a^2 - 8a + 4 = 0# The quadratic formula states: For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by: #x = (-b +- sqrt(b^2 - 4ac))/(2a)# The discriminate is the portion of the quadratic equation within the radical: #color(blue)(b)^2 - 4color(red)(a)color(green)(c)# If the discriminate is: - Positive, you will get two real solutions - Zero you get just ONE solution - Negative you get complex solutions To find the discriminant for this problem substitute: #color(red)(4)# for #color(red)(a)# #color(blue)(-8)# for #color(blue)(b)# #color(green)(4)# for #color(green)(c)# #color(blue)(-8)^2 - (4 * color(red)(4) * color(green)(4)) =># #64 - 64 =># #0# Because the discriminate is #0# there will be just one solution or one root.