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?

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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?

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Answer 1 · 2016-12-23T00:09:12

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

Explanation:

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

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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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?

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Explanation:

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How do you use the discriminant to determine the numbers of solutions of the quadratic equation 2x^2-6x+5 = 02x^2-6x+5 = 0 and whether the solutions are real or complex?

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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?