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There are 5 quadratics below. Four of them have two distinct roots each. The other has only one distinct root; find the value of that root.

 

4x^2 + 16x + 8

-x^2 + 4x + 5

9x^2 - 6x + 1

2x^2 - 8x + 4

225x^2 - 30x + 9

 Jan 30, 2022
 #1
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Find the discriminant (b^2 - 4ac) and see which equation has a discriminant of 0.

 

4x^2 + 16x + 8 ---> 16^2 - 4(4)(8) = 128

-x^2 + 4x + 5 ---> 4^2 - 4(-1)(5) = 36

9x^2 - 6x + 1 ---> (-6)^2 - 4(9)(1) = 0

We know that only one quadratic has one distinct root, so we can stop checking here.

 

9x^2 - 6x + 1 = 0

(3x - 1)^2 = 0

3x - 1 = 0

x = 1/3

 Jan 30, 2022

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