How do you use the discriminant to determine the numbers of solutions of the quadratic equation #2x^2-6x+5 = 0# and whether the solutions are real or complex?

Answer 1

#Delta = -4 < 0#, so this quadratic has a pair of non-Real Complex solutions.

#2x^2-6x+5=0#

is in the form:

#ax^2+bx+c = 0#
with #a=2#, #b=-6# and #c=5#
This has discriminant #Delta# given by the formula:
#Delta = b^2-4ac = (-6)^2-4(2)(5) = 36-40 = -4#
Since #Delta < 0#, this quadratic equation has no Real solutions. It has a complex conjugate pair of distinct non-Real Complex solutions.

We can find the solutions by completing the square:

#0 = 2(2x^2-6x+5)#
#color(white)(0) = 4x^2-12x+10#
#color(white)(0) = 4x^2-12x+9+1#
#color(white)(0) = (2x-3)^2-i^2#
#color(white)(0) = ((2x-3)-i)((2x-3)+i)#
#color(white)(0) = (2x-3-i)(2x-3+i)#

Hence solutions:

#x = 3/2+1/2i" "# and #" "x = 3/2-1/2i#
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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