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This one number can tell you whether the solutions to a quadratic equation are real or non-real, and whether they are distinct or repeated.

Which of the following equations has two distinct real roots?

\[\begin{array} &(A)~x^2-x+1=0 &&(B)~16x^2+8x+1=0\\ (C)~\frac{2}{5}x^2+\frac{3}{10}x+\frac{1}{5}=0 &&(D)~x^2+5x+4=0 \end{array}\]

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If \(a < 3,\) which of the following is true about the quadratic equation: \[x^2+2ax+a^2-3a+11=0 ?\]

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How many distinct real roots does the following equation have: \[(x^2+x+4)(x^2+6x+8)=0?\]

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Which of the following is true about the quadratic equation: \[41x^2-20x+4=5x^2+4x?\]

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