Question #c8554

2 Answers
Feb 16, 2018

Answer:

The discriminant is #-31#, meaning there are #2# complex solutions.

Explanation:

The discriminant is found in the quadratic formula:

#(-b+-sqrt(b^2-4ac))/(2a)#

with the discriminant being

#b^2-4ac#

Let's call the discriminant #d#:

#d<0->"two zeroes that are complex numbers"#

#d=0->"one real zero or a repeated zero"#

#d>0->"two distinct real zeroes"#

We have the equation #x^2-3x+10# already in #ax^2+bx+c# standard form, so plug into the formula:

#(-3)^2-4*1*10#

#9-40=-31#

#d=-31#

The discriminant is #-31#, meaning there are #2# complex solutions.

Bonus: Finding the complex solutions

Plug into the quadratic formula:

#(-(-3)+-sqrt((-3)^2-4*1*10))/(2*1)#

#(3+-sqrt(-31))/2#

Assume #sqrt(-1)# is #i#

#(3+-sqrt(31*-1))/2#

#(3+-sqrt(31)i)/2#

The zeroes are

#(3+sqrt(31)i)/2#, and #(3-sqrt(31)i)/2#

Here is a graph for reference: graph{x^2-3x+10 [-31.76, 32.96, -1.82, 30.53]}

Have a nice day!

Feb 16, 2018

Answer:

The discriminant is #-31#.

Explanation:

To find the discriminant, you have to use the quadratic formula:

#color(white)=x=(-b+-sqrt(b^2-4ac))/(2a)#

The discriminant part is #b^2-4ac#. We need to identify the #a#, #b#, and #c# in our quadratic:

#color(white)=x^2-3x+10#

#a# is 1, #b# is #-3#, and #c# is #10#. Now plug these into the discriminant:

#color(white)(=>)b^2-4ac#

#=>(-3)^2-4(1)(10)#

#=9-40#

#=-31#

The discriminant is #-31#, which means that the quadratic has no real roots.