Suppose that a and b are nonzero real numbers, and that the equation x2+ax+b=0 has solutions a and b. Find the ordered pair (a,b).
as a and b are solutions to x2+ax+b=0we can writex2+ax+b=(x−a)(x−b)=x2−(a+b)x+aba=−(a+b) and b=abb=−2ab=a(−2a)=−2a2−2a=−2a2⇒a=1b=−2a=−2(a,b)=(1,−2)
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