How do you use the discriminant to determine the nature of the solutions given # x^2 – 6x + 5 = 0#?

1 Answer
Apr 27, 2017

Answer:

Please see below.

Explanation:

For an equation #ax^2+bx+c=0#, (assume #a,b# and #c# are rational numbers), the discriminant is #b^2-4ac#.

If #b^2-4ac=0#, we have two roots which are equal i.e. repeated roots.

if #b^2-4ac > 0# and is square of a rational number, then it has two distinct roots, which are rational.

if #b^2-4ac > 0# and but is not square of a rational number, then the two roots are irrational.

if #b^2-4ac < 0#, then the two roots are complex conjugate numbers.

Here, in #x^2-6x+5=0#, we have discriminant #(-6)^2-4xx1xx5=16#, which is square of rational number #2#,

hence roots are two distinct rational numbers.

In fact as #x^2-6x+5=0hArr(x-1)(x-5)-0#, roots are #1# and #5#.