5#ShowThatTheRootsOf x³ + px² + qx + r = 0 are in Arithmetic Progression if 2p³ - 9pq + 27r = 0

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If `2p^3 - 9pq + 27r = 0` then prove that the roots of the equations ` rx^3 - qx^2 + px - 1 = If `2p^3 - 9pq + 27r = 0` then prove that the roots of the equations ` rx^3 - qx^2 + px - 1 =
If the zeros of polynomial f(x)= x3 - px2 + qx - r are in AP, Show that 2p3 - 9pq + 27r = 0 If the zeros of polynomial f(x)= x3 - px2 + qx - r are in AP, Show that 2p3 - 9pq + 27r = 0
If the roots of equation x^3 + px^2 + qx + r =0 are in AP, prove that 2p^3 - 9pq + 27r =0 If the roots of equation x^3 + px^2 + qx + r =0 are in AP, prove that 2p^3 - 9pq + 27r =0
29#Find the Condition that x³ - px² + qx - r = 0 may have the sum of the two of its roots zero 29#Find the Condition that x³ - px² + qx - r = 0 may have the sum of the two of its roots zero
Show that roots of p*square(x) + qx + r = 0 are real if |p/r-7| is greater than equal to 4*sqrt(3). Show that roots of p*square(x) + qx + r = 0 are real if |p/r-7| is greater than equal to 4*sqrt(3).
Find the condition that the roots of the equation x³-px²+qx-r=0may be in A.P. Find the condition that the roots of the equation x³-px²+qx-r=0may be in A.P.
If x^2+px+3=0 and x^2+qx+5=0 and x^2+(p+q)x+24=0 have common negative root, (p+q) is If x^2+px+3=0 and x^2+qx+5=0 and x^2+(p+q)x+24=0 have common negative root, (p+q) is
Show that pq = r if two roots of x^3 + p*x^2 + qx + r = 0 be equal and of opposite sign. Show that pq = r if two roots of x^3 + p*x^2 + qx + r = 0 be equal and of opposite sign.