An algebra problem by Bala vidyadharan

Algebra Level 2

If x^2+ax+1 is a factor of ax^3+bx-c^2 then

b+a+a^2=0 ,a=c b-a+a^3=0 ,a=c b-a+a^2=0, a=c b+a=a^2=0, a=c

Bala Vidyadharan by Bala vidyadharan , 20, India

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1 solution

Use the polynomial multiplexing operator: P ( x ) − a x × ( x 2 + a x + 1 ) = P ( x ) − ( a x 3 + a 2 x 2 + a x ) = − a 2 x 2 + ( b − a ) x − c 2 = Q ( x ) P(x)-ax \times (x^2+ax+1)=P(x) - (ax^{3}+a^{2}x^{2}+ax )=-a^{2}x^{2}+(b-a)x-c^2 = Q(x) Q ( x ) = ( − a 2 ) P ( x ) + ( b − a + a 3 ) x + a 2 − c 2 → b − a + a 3 = 0 , a = c Q(x)=(-a^{2})P(x)+(b-a+a^{3})x+a^{2}-c^{2} \rightarrow \boxed{b-a+a^{3}}=0, a=c

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