Question

if x³+2x²+ax+b has factors x+1 then (a,b)=?​

Answer 1

Answer:

a<=5/4; b<=1/4

Step-by-step explanation:

Since x+1 is a factor, that means x=-1 is a root of the equation.

=> -1³+2(-1)²+a(-1)+b=0

=>-1+2-a+b=0

=>b-a=-1....EQ1

Dividing x³+2x²+ax+b by x+1, we get, x²+x+(a-1)

Since x+1 is a factor of polynomial, => x²+x+(a-1) is also a factor of polynomial.

Therefore, x²+x+(a-1)=0

D= b²-4ac= 1²-4*1*(a-1)=1-4a+4=5-4a

assuming polynomial has real roots,

D>=0

=>5-4a>=0

=>a<=5/4

therefore, b=a-1 (from EQ1)

=> b<=1/4

Answer 2

Step-by-step explanation:

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