a = 36, b = -12â(11), c = 11 this is looking obvious but let's go through the motions.
Discriminant = b^2 - 4ac
discriminant = (-12â(11))^2 - 4(36)(11)
discriminant = 144*11 - 144*11
discriminant = 0
Therefore there is ONE real root.
Just for fun (I know you didn't ask for it) let's figure out what that one root is.
(-b +/- sqrt(discriminant))/2a
- (-12â(11)) / 2*36
12â(11) / 72
â(11)/6
Edit to cidyah - you drew the wrong conclusion because of a truncation error, that is why as soon as I realised b was irrational I didn't bother trying to express it as a decimal, luckily on a calculator if you don't round it off you will get the right answer. Here are my calculations try it yourself on the windows calculator.
b = exactly -12â(11) which is APPROXIMATELY -39.799497484264798189379192840048
You rounded this to -39.799 which you used to give an answer to the discriminant of -0.0395989999, thus introducing a truncation error which is why you thought the discriminant was negative and nonzero. -12â(11) is irrational and can't be expressed exactly as a decimal however if you leave -12â(11) in your calculator without rounding you will get -39.799497484264798189379192840048 which when squared = 1584
Now calculate the discriminant with b^2 = 1584 and you get
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solution:
x₁ = x₂ = 0.55277079839256664151915545611178 ........
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a = 36, b = -12â(11), c = 11 this is looking obvious but let's go through the motions.
Discriminant = b^2 - 4ac
discriminant = (-12â(11))^2 - 4(36)(11)
discriminant = 144*11 - 144*11
discriminant = 0
Therefore there is ONE real root.
Just for fun (I know you didn't ask for it) let's figure out what that one root is.
(-b +/- sqrt(discriminant))/2a
- (-12â(11)) / 2*36
12â(11) / 72
â(11)/6
Edit to cidyah - you drew the wrong conclusion because of a truncation error, that is why as soon as I realised b was irrational I didn't bother trying to express it as a decimal, luckily on a calculator if you don't round it off you will get the right answer. Here are my calculations try it yourself on the windows calculator.
b = exactly -12â(11) which is APPROXIMATELY -39.799497484264798189379192840048
You rounded this to -39.799 which you used to give an answer to the discriminant of -0.0395989999, thus introducing a truncation error which is why you thought the discriminant was negative and nonzero. -12â(11) is irrational and can't be expressed exactly as a decimal however if you leave -12â(11) in your calculator without rounding you will get -39.799497484264798189379192840048 which when squared = 1584
Now calculate the discriminant with b^2 = 1584 and you get
1584 - 4*36*11 = 1584 - 1584 = 0.
This equation is of form ax^2+bx+c
a = 36 b = -39.799 c = 11
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[39.799 +/-sqrt(-39.799^2-4(36)(11)]/(2)(36)
discriminant is b^2-4ac =-0.0395989999
Since the discriminant is negative, the roots are complex since the roots occur in pairs for a quadratic equation.
The above answer is incorrect: ignore: