Let a1 a2 a3 a4 a5 a6 p = a 1+ a 2+ a 3+ ldots ldots+ a 6 q = a 1 a 3+ a 3 a 5+ a 5 a 1+ a 2 a 4+ a 4 a 6+ a 6 a 2 r=a1 a3 a5+a2 a4 a6, then the equation 2 x3-p x2+q x-r=0 has

Question

Let a1 >a2 >a3 >a4 >a5 >a6 p = a 1+ a 2+ a 3+ ldots ldots+ a 6 q = a 1 a 3+ a 3 a 5+ a 5 a 1+ a 2 a 4+ a 4 a 6+ a 6 a 2 r=a1 a3 a5+a2 a4 a6, then the equation 2 x3-p x2+q x-r=0 has (A) one root between (a1, a2) (B) two roots between ( a 1, a 3) (C) two roots lies between (a1, a4) (D) two roots lies between (a3, a5)

Tardigrade Admin · Accepted Answer

Correct answer is (a) one root between (a1, a2)Correct answer is (c) two roots lies between (a1, a4)

Q. Let $a_{1} > a_{2} > a_{3} > a_{4} > a_{5} > a_{6}$ $p = a_{1} + a_{2} + a_{3} + \dots\dots + a_{6}$ $q = a_{1} a_{3} + a_{3} a_{5} + a_{5} a_{1} + a_{2} a_{4} + a_{4} a_{6} + a_{6} a_{2}$ $r = a_{1} a_{3} a_{5} + a_{2} a_{4} a_{6}$ , then the equation $2 x^{3} - p x^{2} + q x - r = 0$ has

one root between $(a_{1}, a_{2})$

two roots between $(a_{1}, a_{3})$

two roots lies between $(a_{1}, a_{4})$

two roots lies between $(a_{3}, a_{5})$

Correct answer is (a) one root between $(a_{1}, a_{2})$ Correct answer is (c) two roots lies between $(a_{1}, a_{4})$

Q. Let a1​>a2​>a3​>a4​>a5​>a6​ p=a1​+a2​+a3​+……+a6​ q=a1​a3​+a3​a5​+a5​a1​+a2​a4​+a4​a6​+a6​a2​ r=a1​a3​a5​+a2​a4​a6​, then the equation 2x3−px2+qx−r=0 has

one root between (a1​,a2​)

two roots between (a1​,a3​)

two roots lies between (a1​,a4​)

two roots lies between (a3​,a5​)