Find the discriminant of quadratic equation 2x²-5x+5 =0.
Answers
Answer:
For this quadratic, Δ = − 15 , which means that the equation has no real solutions, but it does have two distinct complex ones.
Explanation:
The general form for a quadratic equation is
a x ^2 + b x + c = 0
The general form of the discriminant looks like this
Δ = b^ 2 - 4 ⋅ a ⋅ c
Your equation looks like this
2 x ^2 + 5x + 5 = 0
which means that you have
a = 2
b = 5
c = 5
The discriminant will thus be equal to
Δ = 5^ 2 − 4 ⋅ 2 ⋅ 5
Δ = 25 − 40 = − 15
The two solutions for a general quadratic are
x 1 , 2 = − b ± √ Δ
----------------
2 a
When Δ < 0 , such as you have here, the equation is said to have no real solutions, since you're extracting the square root from a negative number.
However, it does have two distinct complex solutions that have the general form
x 1 , 2 = − b ± i √ − Δ
------------------- when Δ < 0
2 a,
In your case, these solutions are
x 1 ,2
= − 5 ± √ − 15
------------------
4
= x 1 = − 5 + i √ 15
---------------------
4
x 2 = - 5 − i √ 15
--------------------
4
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