For which values of a and b the zeroes of q(x)=x3-2x2-x+a are also the zeroes of polynomial p(x)=x5-2x4-10x3+20x2+9x+b
Answers
Given : (x)=x³-2x²-x+a are also the zeroes of polynomial p(x)=x⁵-2x⁴-10x³+20x²+9x+b
To find Values of a & b
Solution:
zeroes of q(x)=x³-2x²-x+a are also the zeroes of polynomial p(x)=x⁵-2x⁴-10x³+20x²+9x+b
x² - 9
___________________
x³-2x²-x+a _| x⁵-2x⁴-10x³+20x²+9x+b |_
x⁵ - 2x⁴ -x³ + ax²
___________
-9x³ + (20-a)x²+9x+b
-9x³ + 18x² + 9x - 9a
________________
(2 - a)x² + (b + 9a)
(2 - a)x² + (b + 9a) = 0
also x² - 9 is factor of x⁵-2x⁴-10x³+20x²+9x+b
=> x = ± 3
=> 3⁵-2*3⁴-10*3³+20*3²+9*3+b = 0
=> 243 - 162 - 270 + 180 + 27 + b = 0
=> b = - 18
(2 - a)x² + (b + 9a) = 0
=> (2 - a)x² -18 + 9a = 0
=> (2 - a)x² - 9(2 - a) =
=> (2 - a)(x² - 9) = 0
=> a = 2
a = 2 & b = - 18
Learn More:
Obtain all other zeros of x 4 + 4 x cube minus 2 x square - 20 x ...
https://brainly.in/question/9634458
obtain all the zeros of the polynomial 8x^4+8x^3-18x^2-20x-5 if two ...
https://brainly.in/question/7286826
33.If two zeroes of polynomial P(x) = 2x4 + 10x3 + 5x2 – 35x – 42 are
https://brainly.in/question/14933868