+22 Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.\(\begin{align*} &-x^2 + 18x + 81 \\ &3x^2 - 3x - 168 \\ &x^2 - 4x - 4 \\ &25x^2 - 30x + 9 \\ &x^2 - 14x + 24 \end{align*}\)
+14915 Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.
\(\begin{align*} &(1)-x^2 + 18x + 81 \\ &(2)\ 3x^2 - 3x - 168 \\ &(3)\ x^2 - 4x - 4 \\ &{\color{blue}(4)\ 25x^2 - 30x + 9} \\ &(5)\ x^2 - 14x + 24 \end{align*} \)
a b c
\(x = {-b \pm \sqrt{{\ \color{blue}b^2-4ac}} \over 2a}\)
\(A \ quadratic\ equation\ has\ a\ double\ root\\ \color{blue} if\ \ b^2-4ac=0\).
(1) \(18^2-4 *(-1)*81=648 \neq 0\)
(2) \(3^2-4*(3)*(-168)=2025\neq 0\)
(3) \(4^2-4*1*(-4)=32\neq 0\)
(4) \(30^2-4*25*9=0\)
(5) \(14^2-4*1*24=100\neq0\)
\((4)\ 25x^2 - 30x + 9\)
\(x = {30 \pm \sqrt{30^2-4*25*9} \over 2*25}\)
\(x_4=0.6\)
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