(x)= ax^3+bx^2+cx+d is a polynomial, a) if (x-1) is a factor of p(x) then what is a+b+c+d, b) if ( x+1) is a factor of p(x) then write the relation between the coefficients a,b,c and d 3)write a third degree polynomial having two factors (x+1)(x-1)
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Answer:
Correct option is A)
Given that x
2
+px+1 is a factor of ax
3
+bx+c.
Let ax
3
+bx+c=(x
2
+px+1)(ax+λ), where λ is a constant.
Then equating the coefficients of line powers of x on both sides, we get
0=ap+λ,b=pλ+a,c=λ
⇒p=−
a
λ
=−
a
c
Hence,
b=(−
a
c
)c+a
⇒ab=a
2
−c
2
Step-by-step explanation:
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