The equation x^2-ax+b=0 and x^3-px+qx=0
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Step-by-step explanation:
p(x) = x³ - px + qx
q(x) = x² - ax + b
g(x) = cx + d
p(x) = q(x)(gx)
=> x³ - px + qx = (x² - ax + b)(cx + d)
=> x³ - px + qx = cx³ +x²(d -ca) + x(bc -ad) + bd
Equating powers
c = 1
d - ca = 0
=> d - a = 0
=> d = a
=> g(x) = (x + a)
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