How do you find value of discriminant then describe number and type of solutions for #x^2 - 6x +3 = 0#?

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Answer 1 · 2016-07-06T21:20:19

The roots are real, different and irrational.

We can work out what type of roots an equation has by finding the discriminant. It is called #Delta " (delta)"#

In #ax^2 + bx + c " "Delta = b^2 -4ac#,

If #Delta < 0, #then the roots are imaginary, (non-real).

If #Delta = 0, #then the roots are real and equal. (ie one root)

If #Delta > 0,#then the roots are real, different and irrational.

If #Delta >0, #and is a perfect square, (1, 4, 9, 16 ......) then the roots are real, different and rational.

In this example: #Delta = (-6)^2 - 4(1)(3) = 24#

The roots are real, different and irrational.