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Vieta's formula relates the coefficients of polynomials to the sum and products of their roots. This can provide a shortcut to finding solutions in more complicated algebraic polynomials.

Which of the following expresses the quadratic equation whose roots are \(p\) and \(6\)?

A) \( x^2 - 6p x + (6 + p) = 0 \)

B) \( x^2 + 6p x - (6+b) = 0 \)

C) \( x^2 + (6 + p) x - 6p = 0 \)

D) \( x^2 - (6+p) x + 6p = 0 \)

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In the above diagram, \(AB\) is a diameter of the circle with radius \(21\) and \(CD\) intersects \(AB\) at point \(P.\) Suppose that \(\lvert \overline{CP} \rvert =8\) and \( \lvert \overline{DP} \rvert=12.\) If the quadratic equation whose two roots are \(\lvert \overline{AP} \rvert\) and \( \lvert \overline{BP} \rvert\) can be expressed as \(x^2+ax+b=0,\) what is the value of \(a+b?\)

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Which of the following expresses the quadratic equation whose roots are \(4\) and \(-6\)?

A) \( x^2 + 2 x + 24 = 0 \)

B) \( x^2 - 2 x + 24 = 0 \)

C) \( x^2 + 2 x - 24 = 0 \)

D) \( x^2 - 2 x - 24 = 0 \)

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