Algebra

Vieta's Formula

Vieta's Formula - Forming Quadratics

         

Which of the following expresses the quadratic equation whose roots are pp and 66?

A) x26px+(6+p)=0 x^2 - 6p x + (6 + p) = 0
B) x2+6px(6+b)=0 x^2 + 6p x - (6+b) = 0
C) x2+(6+p)x6p=0 x^2 + (6 + p) x - 6p = 0
D) x2(6+p)x+6p=0 x^2 - (6+p) x + 6p = 0

In the above diagram, ABAB is a diameter of the circle with radius 2121 and CDCD intersects ABAB at point P.P. Suppose that CP=8\lvert \overline{CP} \rvert =8 and DP=12. \lvert \overline{DP} \rvert=12. If the quadratic equation whose two roots are AP\lvert \overline{AP} \rvert and BP \lvert \overline{BP} \rvert can be expressed as x2+ax+b=0,x^2+ax+b=0, what is the value of a+b?a+b?

Which of the following expresses the quadratic equation whose roots are 44 and 6-6?

A) x2+2x+24=0 x^2 + 2 x + 24 = 0
B) x22x+24=0 x^2 - 2 x + 24 = 0
C) x2+2x24=0 x^2 + 2 x - 24 = 0
D) x22x24=0 x^2 - 2 x - 24 = 0

Let α\alpha and β\beta be the two roots of the quadratic equation x2mx+n=0,x^2-mx+n=0, and α+β\alpha+\beta and αβ\alpha\beta be the two roots of the quadratic equation x28x+1=0.x^2-8x+1=0. Then what is the value of m3+n3?m^3+n^3 ?

Let α\alpha and β\beta be the two roots of the quadration x22x2=0.x^2-2x-2=0. If the quadratic equation whose two roots are α3\alpha^3 and β3\beta^3 can be expressed as x2+ax+b=0,x^2+ax+b=0, what is the value of 3ab?3ab?

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