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Problem Solving (PS) | If there are two unique solutions to the equation x^2 + bx + 9 = 0, wh

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Bunuel wrote:

If there are two unique solutions to the equation x^2 + bx + 9 = 0, which of the following could not be a value of b?

A. -10
B. -6.5
C. -6
D. 6.5
E. 10

The expression\(b^2 - 4ac\) is the "discriminant" of the quadratic equation.

If\(b^2 - 4ac > 0\) , there are two solutions

If\(b^2 - 4ac = 0\) , there is one solution

If\(b^2 - 4ac < 0\) , there are no solutions

There are two unique solutions here so
\(b^2 - 4ac > 0\)\(a = 1\)
\(c = 9\)\(4ac = 36\)

\(b^2 - 36 > 0\)\(b^2 > 36\)

\( \sqrt{b^2} >\sqrt{36} \)
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