The quadratic equation with a repeated root is:
8*x^2 - 32*x +32
And the repeated root is x = 2
What is the repeated root?
For a quadratic equation:
0 = a*x^2 + b*x + c
We define the discriminant as:
D = b^2 - 4ac
If D = 0, we have only one real root (or two repeated roots). Then we just need to see which of the given quadratic equations has a discriminant of zero.
1) -x^2 + 18x + 81
The discriminant is:
D = 18^2 - 4*(-1)*81 = 648
2) 3x^2 - 6x + 9
The discriminant is:
D = (-6)^2 - 4*3*9 = -72
3) 8*x^2 - 32*x +32
The discriminant is:
D = (-32)^2 - 4*8*32 = 0
So this is the one with a discriminant of zero.
The roots are given by:
8*x^2 - 32*x +32 = 0
Using Bhaskara's formula we will get:
x = (- (-32) ± √( (-32)^2 - 4*8*32))/(2*8)
x = (32/16) = 2
The repeated root is x = 2
If you want to learn more about quadratic equations:
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