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.
\( 4x^2 +16x - 9\\ 2x^2 + 80x + 400\\ x^2 - 6x - 9\\ 4x^2 - 12x + 9\\ {-x^2 + 14x + 49} \)
+9466 discriminant of first one = 162 - 4(4)(-9) = 400 ≠ 0
discriminant of second one = 802 - 4(2)(400) = 3200 ≠ 0
discriminant of third one = (-6)2 - 4(1)(-9) = 72 ≠ 0
discriminant of fourth one = (-12)2 - 4(4)(9) = 0
discrimimant of fifth one = (14)2 - 4(-1)(49) = 392 ≠ 0
The fourth one is the quadratic with one distinct root.
4x2 - 12x + 9 = 0 when
x = \(\frac{-(-12)\pm\sqrt{(-12)^2-4(4)(9)}}{2(4)}\ =\ \frac{12\pm0}{8}\ =\ \frac{12}{8}\ =\ \frac32\)
Here's a graph of all of them: https://www.desmos.com/calculator/vrjvowhts0
