Find the constants a and b such that x = -1 and x = 1 are both solutions to the equation ax^2 + bx + 2 = 0.
+179 \(a = -2, b=0\)
To obtain this, simply put x=1 into \(ax^2 +bx+2 = 0\), getting \(a+b = -2\)
Afterward, put x= -1 into \(ax^2+bx+2 = 0\), getting, \(a-b=-2.\)
Adding the two equations, we have \(2a = -4\), so \(a = -2\), and because \(a+b = 0\), and \(a = -2, b=0\)
