x+a is a common factor of x²+px + q and 2² lx+m
find a
Answers
a = m-1 / p+l
Step-by-step explanation:
Note: There is an error in the question. The second polynomial should be x² + lx + m. 2² is an error. Please see solution below.
(x+ a) is a factor of x²+px + q.
Substituting x = -a in x² + px + q = 0, we get:
(-a)² +p(-a) + q = 0
a² + ap + q = 0 ----------------(1)
(x+ a) is a factor x² + lx + m
Substituting x = -a in x² + lx+m, we get:
(-a)² + l(-a) + m = 0
a² -al + m = 0 ----------(2)
Subtracting 2 from 1, we get:
ap + al + q - m = 0
a (p + l) = m-1
a = m-1 / p+l
Given : x+a is a common factor of x²+px + q and x² + lx+m
To find : a
Solution:
x+a is a common factor of x²+px + q and x² + lx+m
=> x + a = 0
=> x = - a is one of the zero
=> (-a)² +pa + q = 0 & (-a)² +la + m = 0
=> a² +pa + q = 0 & a² +la + m = 0
=> a² +pa + q = a² +la + m
=> pa + q = la + m
=> a(p - l) = m - q
=> a = (m - q)/(p - l)
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