Suppose the cubic `x^3-px+q` has three distinct real roots when `p lt 0 and p lt 0.` then which one of the following holds ? (a) The cubic has minima at `-sqrt(p/3)` and maxima at `sqrt(p/3)` (b) The cubic has minima at both `sqrt(p/3) and -sqrt(p/3)` (c) The cubic has maxima at both `sqrt(p/3) and -sqrt(p/3)` (d) The cubic has minima at `sqrt(p/3)` and maxima `-sqrt(p/3)`

Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0 and qgt0 . Then which one of the following holds?

Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . Then which one of the following holds ?

Suppose the cube x^3""p x""+""q has three distinct real roots where p"">""0 and q"">""0 . Then which one of the following holds? (1) The cubic has minima at ( 2) (3)sqrt(( 4) (5) (6) p/( 7)3( 8) (9) (10))( 11) (12) (13) and maxima at ( 14) (15)-sqrt(( 16) (17) (18) p/( 19)3( 20) (21) (22))( 23) (24) (26) The cubic has minima at ( 27) (28)-sqrt(( 29) (30) (31) p/( 32)3( 33) (34) (35))( 36) (37) (38) and maxima at ( 39) (40)sqrt(( 41) (42) (43) p/( 44)3( 45) (46) (47))( 48) (49) (51) The cubic has minima at both ( 52) (53)sqrt(( 54) (55) (56) p/( 57)3( 58) (59) (60))( 61) (62) (63) and ( 64) (65)-sqrt(( 66) (67) (68) p/( 69)3( 70) (71) (72))( 73) (74) (76) The cubic has maxima at both ( 77) (78)sqrt(( 79) (80) (81) p/( 82)3( 83) (84) (85))( 86) (87) (88) and ( 89) (90)-sqrt(( 91) (92) (93) p/( 94)3( 95) (96) (97))( 98) (99) (100)

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .

If p and q are positive integers, then which one of the following equations has p-sqrt(q) as one of its roots ?

(sqrt3+i)^100=2^99(p+iq) then p and q are the roots of which of the following quadratic equation?

The value of sqrt(P^3sqrt(P^3 sqrt(P^3))) is -

Let 'p' & 'q' be real numbers . Prove that the cubic y = x^(3) + p x + q has three distinct real roots, if 4 p^(3) + 27 q^(2) lt 0 .

If P+Q=(7 pi)/(6), then the value of (sqrt(3)+tan P)(sqrt(3)+tan Q) is equal to