What is the value of the discriminant in the equation shown below?
x^2-6x+4=0

Question

What is the value of the discriminant in the equation shown below?
x^2-6x+4=0

mathmale · Answer

Compare your equation to ax^2 + bx + c = 0.  What are the values of a, b and c?

a=?
b=?
c=?

sharkfinsoup · Answer

a=x^2
b=-6x
c=4

mathmale · Answer

a, b and c are called "coefficients."  Focus on the 1 in 1x^2, the -6 in -6x, and the 4.

a=1
b=-6
c=4.

Again, do not include the powers of x:  x^2, x, x^0.

Now, what is the value of b^2?

sharkfinsoup · Answer

36

mathmale · Answer

That's right:  (-6)^2=36.

What is the value of a*c?  (a times c)

sharkfinsoup · Answer

4

mathmale · Answer

Good!  Now please write out "b^2 - 4ac," using your previous calculations.

b^2-4ac= ?

sharkfinsoup · Answer

36-16=20

mathmale · Answer

You're doing great.  That 's the "discriminant" of the given equation.  You're done.

When told to find the "discriminant," calculate b^2-4ac.

sharkfinsoup · Answer

oh ok

sharkfinsoup · Answer

so 20 is the answer

mathmale · Answer

Were you to continue, to find the two roots of the given equation, you'd evaluate$$x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$$

mathmale · Answer

Yes, the discriminant here is 20, and you're done.  But be sure you understand that b^2-4ac is part of the quadratic formula, given above, by which we find the "roots" or "zeros" of the given quadratic equation.

sharkfinsoup · Answer

Thank you so much for the explanation

mathmale · Answer

Best to know what you can do with a result such as your discriminant, '20.'
You're welcome!