SOLUTION: Is this correct statement that "Equations {{{ x^2 + x + a = 0 }}} and {{{ x^2 + ax + 1 = 0 }}} have a common real point for exactly one value of a"?

Question 1184293: Is this correct statement that "Equations and have a common real point for exactly one value of a"?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Is this correct statement that equations
and

have a common real point for exactly one value of "?
check if there is a value of for what discriminants are equal to zero

discriminant:
.........in your case , and

discriminant:
.........in your case, and

or

check if any of will give us one solution:

________________________-> no solution exist

_______________-> no solution exist

_______________ ->solution
parabolas have a common real point for exactly one value of
so, the statement above is correct

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For what value(s) of the coefficient a do the equations x^2-ax + 1=0 and x^2-x+a=0 have a (answered by ankor@dixie-net.com)