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if x^2+px+1 is a factor of expression ax^3+bx^2+c then prove that a^2_c^2=_bc

if x^2+px+1 is a factor of expression ax^3+bx^2+c then prove that a^2_c^2=_bc

Grade:

2 Answers

praveen dhanalakota
16 Points
7 years ago

ax3+bx2+c=(x2+px+c)(kx+m) where kx+m is a linear factor

expandinding the above and comparing coefficients of same powers of x we get

p=-a/c,ap+c=b,put p=-a/c in ap+c=b

we get -a2/c+c=b

-a2+c2=bc

so a2-c2=-bc

hence proved

India VK
42 Points
7 years ago

suppose (ex+f) is the other root. Therefore,

(x^2+px+1)(ex + f) = ax^3 + bx^2 + c


Now equate coefficients and eliminate e,f.

 

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