If two roots of the equation x^3-p x^2+q x-r=0 are equal in magnitude but opposite in sign, then:...

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If two roots of the equation x^3-p x^2+q x-r=0,(r ≠ 0) are equal in magnitude but opposite in sig...If two roots of the equation x^3-p x^2+q x-r=0,(r ≠ 0) are equal in magnitude but opposite in sig...
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.
If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then | 11 | QUADRATIC EXP...If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then | 11 | QUADRATIC EXP...
If be roots of cubic of cubic x^3-px^2+qx-r=;form the equation whose roots are :If be roots of cubic of cubic x^3-px^2+qx-r=;form the equation whose roots are :
If the roots of equation x^3 + px^2 + qx + r =0 are in AP, prove that 2p^3 - 9pq + 27r =0If the roots of equation x^3 + px^2 + qx + r =0 are in AP, prove that 2p^3 - 9pq + 27r =0
If p, q, r are in GP and the equations px^2 + qx + r=0 and dx^2 + 2ex + f=0 have a common rootIf p, q, r are in GP and the equations px^2 + qx + r=0 and dx^2 + 2ex + f=0 have a common root
If a, b be two real roots of the x^3 + px^2 + qx + r = 0 relation ab + 1 =0, r^2 + pr + q + 1 = 0If a, b be two real roots of the x^3 + px^2 + qx + r = 0 relation ab + 1 =0, r^2 + pr + q + 1 = 0
if one root of the equation x^3+px^2+qx+r=0 is equal to the sum of the other two then ST p^3+8r=4pqif one root of the equation x^3+px^2+qx+r=0 is equal to the sum of the other two then ST p^3+8r=4pq