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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

Feb 13, 2022

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Find the value of that root.

Hello Guest!

$$ax^2+bx+c$$

In the searched quadratic must apply:   $$b^2-4ac=0$$

$$4x^2 + 16x + 8\ |\ b^2-4ac\neq 0\\ x^2 + 4x + 5\ |\ b^2-4ac\neq 0\\ 9x^2 - 6x + 1\ |\ \color{blue}b^2-4ac=(-6)^2-4\cdot 9\cdot 1=0\\ 2x^2 - 8x + 4\ |\ b^2-4ac\neq 0\\ 225x^2 - 30x + 9\ |\ \color{red}b^2-4ac< 0$$

$$\color{blue}9x^2 - 6x + 1=0\\ x = {6 \pm \sqrt{36-4\cdot 9\cdot 1} \over 2\cdot 9}\\The\ value\ is\\ \color{blue}x=\dfrac{1}{3}$$