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
+14913 Find the value of that root.
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\(ax^2+bx+c\)
In the searched quadratic must apply: \(b^2-4ac=0 \)
\(4x^2 + 16x + 8\ |\ b^2-4ac\neq 0\\ x^2 + 4x + 5\ |\ b^2-4ac\neq 0\\ 9x^2 - 6x + 1\ |\ \color{blue}b^2-4ac=(-6)^2-4\cdot 9\cdot 1=0\\ 2x^2 - 8x + 4\ |\ b^2-4ac\neq 0\\ 225x^2 - 30x + 9\ |\ \color{red}b^2-4ac< 0 \)
The searched quadratic function is:
\(\color{blue}9x^2 - 6x + 1=0\\ x = {6 \pm \sqrt{36-4\cdot 9\cdot 1} \over 2\cdot 9}\\The\ value\ is\\ \color{blue}x=\dfrac{1}{3}\)
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