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# Help

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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.

\begin{align*} &4x^2 +16x - 9\\ &2x^2 + 80x + 400\\ &x^2 - 6x - 9\\ &4x^2 - 12x + 9\\ &{-x^2 + 14x + 49} \end{align*}

Guest Jan 11, 2018
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A quadratic will have only one root  when the discriminant, b^2  - 4ac  = 0

4x^2 + 16x - 9    ⇒   16^2   - 4(4)(-9)  > 0

2x^2 + 80x + 400  ⇒    80^2  - 4(2 )( 400) > 0

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

4x^2 - 12x + 9   ⇒   (-12)^2  - 4 (4)(9)  =  0

-x^2 + 14x + 49  ⇒  (14)^2  - 4(-1)(49)  > 0

So

4x^2  - 12x +  9  =  0  factors as

(2x - 3) (2x - 3)  = 0

(2x - 3)^2  =  0

And this is true when   x  =  3/2

CPhill  Jan 11, 2018

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