If the equation mentioned below has exactly 4 positive roots, then which
of
following can be the value of (P. Q) ?
X5 - 5x4 - 15x3 + PX? +QX + 120 = 0
O (-125, 226)
O (-226, -226)
O
(125,-226)
O (125, 125)
O (125, 226)
Answers
Answer:
hfutsjgkfuchch7fbf fh7yjcgyur
Given : equation mentioned below has exactly 4 positive roots
X⁵ - 5x⁴ - 15x³ + PX² +QX + 120 = 0
To Find : which of following can be the value of (P. Q)
O (-125, 226)
O (-226, -226)
O (125,-226)
O (125, 125)
O (125, 226)
Solution:
Possible roots can be
1 , 2 , 3 , 4 and - 5
Sum of roots = 5 = (-)(-5)/1 = 5 Satisfied
Product of roots = -120 = - 120/1 = - 120 Satisfied
Summation of product of two roots at a time
= 2 + 3 + 4 - 5 + 6 + 8 - 10 + 12 - 15 - 20
= - 15 ( satisfied)
Product of 3 roots at a time = - P
6 + 8 - 10 + 12 - 15 -20 + 24 - 30 - 40 - 60 = -125
-P = - 125
=> P = 125
Product of 4 roots at a time = Q
24 - 30 -40 -60 - 120 = - 226
=> Q = - 226
the value of (P. Q) ( 125 , - 226)
x⁵ - 5x⁴ - 15x³ + 125x² -226x + 120 = 0
(x - 1)(x -2)(x -3)(x-4)(x + 5) = 0
Learn More
Obtain all other zeros of x 4 + 4 x cube minus 2 x square - 20 x ...
brainly.in/question/9634458
obtain all the zeros of the polynomial 8x^4+8x^3-18x^2-20x-5 if two ...
brainly.in/question/7286826
33.If two zeroes of polynomial P(x) = 2x4 + 10x3 + 5x2 – 35x – 42 are
brainly.in/question/14933868