Find the value of the discriminant and state whether the equation has two distinct real roots,two equal real roots or no real roots.
2x2=0.25x(1-x)
F4 maths (1 question)
2007-09-23 2:48 am
回答 (3)
2007-09-23 2:57 am
✔ 最佳答案
2x^2=0.25x-0.25x^22.25x^2-0.25x=0
Discriminant= (-0.250^2-4(2.25)(0)
=0.0625-0
=0.0625>0
Two distinct Root
參考: myself,hope it can help you
2007-09-24 12:02 am
It will be better if you multiply both sides by 4 to remove any decimal numbers...
2x^2 = 0.25x(1-x)
8x^2 = x(1-x)
8x^2 = x - x^2
9x^2 = x
9x^2 - x = 0 (Key step: Don't divide any unknown for both sides!!!)
x(9x-1) = 0 (x is common factor)
x = 0 or x = 1/9
Without finding the value of discriminant, the equation has 2 distinct roots
If we have to find the discriminant, start from this 9x^2 - x = 0
From this equation, a=9, b=-1, c=0
Discriminant = b^2 - 4ac
= (-1)^2 - 4(9)(0)
= 1
> 0
Thus the equation has 2 distinct roots
2x^2 = 0.25x(1-x)
8x^2 = x(1-x)
8x^2 = x - x^2
9x^2 = x
9x^2 - x = 0 (Key step: Don't divide any unknown for both sides!!!)
x(9x-1) = 0 (x is common factor)
x = 0 or x = 1/9
Without finding the value of discriminant, the equation has 2 distinct roots
If we have to find the discriminant, start from this 9x^2 - x = 0
From this equation, a=9, b=-1, c=0
Discriminant = b^2 - 4ac
= (-1)^2 - 4(9)(0)
= 1
> 0
Thus the equation has 2 distinct roots
參考: Me
2007-09-23 4:07 am
2x^2=0.25x(1-x)
8x^2=x(1-x)
8x^2=x-x^2
9x^2-x=0
x=0 or x=1/9
2007-09-22 20:09:04 補充：
so it has two distinct real roots
8x^2=x(1-x)
8x^2=x-x^2
9x^2-x=0
x=0 or x=1/9
2007-09-22 20:09:04 補充：
so it has two distinct real roots
收錄日期: 2021-04-13 19:03:11
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