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Find the constants a and b such that x = -1 and x = 1 are both solutions to the equation ax^2 + bx + 2 = 0.

 Jun 5, 2021
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\(a = -2, b=0\)

 

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 \(a = -2, b=0\)

 Jun 5, 2021

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