How do you find the value of the discriminant and determine the nature of the roots #2p^2+5p-4#?

1 Answer
Jun 6, 2017

Answer:

#Delta = 57 > 0# is not a perfect square, so the zeros are distinct, real and irrational.

Explanation:

Given:

#2p^2+5p-4#

Note that this is written in standard form:

#ap^2+bp+c#

with #a=2#, #b=5# and #c=-4#

The discriminant #Delta# is given by the formula:

#Delta = b^2-4ac#

#color(white)(Delta) = color(blue)(5)^2-4(color(blue)(2))(color(blue)(-4))#

#color(white)(Delta) = 25+32#

#color(white)(Delta) = 57#

Since #Delta > 0# the given quadratic has two distinct real zeros. Since #Delta = 57# is not a perfect square, those zeros are irrational.

The zeros of #2p^2+5p-4# are the roots of the equation:

#2p^2+5p-4 = 0#