If 1 is a root of the quadratic equation 3x2+ax-2=0 and the quadratic equation a(ax2+6x)-b=0 has equal roots find the value of b?
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Since 1 is a root,
3×1^2 + a×1 - 2 = 0
a = -1.
Thus second equation is
-1×(-1x^2+6x)-b=0
i.e., x^2 - 6x -b = 0
This equation has equal roots, so discriminant = 0.
(-6)^2-4×1×-b = 0
b = -36/4 = -9
3×1^2 + a×1 - 2 = 0
a = -1.
Thus second equation is
-1×(-1x^2+6x)-b=0
i.e., x^2 - 6x -b = 0
This equation has equal roots, so discriminant = 0.
(-6)^2-4×1×-b = 0
b = -36/4 = -9
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