Question

find the values of a and b such that (X + 1 )and (x - 3) are the factor of the polynomial
$x {}^{3 } + ax {}^{2} + 5x + b$
ANSWER
a = -6, b = 12

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Answer 1

Answer:

a/b×100=6/12×100=15

Step-by-step explanation:

Answer by my teacher

Answer 2

QUESTION:-

find the values of a and b such that (X + 1 )and (x - 3) are the factor of the polynomial

x³+ax²+5x+b

[NOTE-$x^3+ax^2+5x+b$=x³+ax²+5x+b ]

EXPLANATION:-

Let p(x)=x³+ax²+5x+b

Since x+1 is a factor then :-

x+1=0

x=-1 is a zero of the polynomial

Since x=-1 is the zero of the polynomial,so '

p(-1)=0

Let's find thee value of p(-1)

p(-1)=(-1)³+a(-1)²+5(-1)+b

p(-1)=-1+a-5+b

p(-1)=-6+a+b

Since p(-1)=0

0=-6+a+b

6=a+b------eq-1

Similarily:-

x-3=0

x=3 is the zero of the polynomia;

p(3)=0 (SINCE 3 IS THE ZERO OF THE POLYNOMIAL)

p(3)=(3)³+a(3)²+5(3)+b

p(3)=27+9a+15+b

p(3)=42+9a+b

[p(3)=0]

0=42+9a+b

-42=9a+b------eq-2

From eq-1 and 2

6=a+b

b=6-a

Put b=6-a in eq-2

-42=9a+6-a

-42=8a+6

-42-6=8a

-48=8a

a=-48/8

a=-6

Put a=-6 in eq-1

a+b=6

-6+b=6

b=6+6

b=12

So b=12

Hence,

a=-6 and b=12

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