Question

Find the value of the variable a and b. if the polynomial
p(x)=x3+ax2+bx+5 is divided by (x+1) and (x-1) both​

Answer 1

Answer:

a = -5

b = -1

Step-by-step explanation:

x+1=0

x = -1

p(-1) = (-1)³+a.(-1)²+b(-1)+5=0

-1+a-b+5=0

a-b= 1-5

a-b= -4 ............(equation 1)

x-1=0

x=1

p(1) = 1³+a.1²+b.1+5 = 0

1+a+b+5 = 0

a+b = -6 ...........(equation 2)

Adding equation 1 and 2

a-b = -4

a+b = -6

2a = -10

a = -5

a+b = -6

b= -6-(-5)

b = -6+5

b = -1

I hope it is useful....

Answer 2

Answer:

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Step-by-step explanation:

p(x) = x³+ax²+bx+5

( i ) g(x) = (x+1 )

( ii) g(x) = ( x- 1 )

(i)

g(x) = (x+1 )

(x+1)=0

x= -1

p(-1) = (-1)³+ a( -1)² +b (-1) +5

= (-1) +a -b +5

= 4 + a - b.................. ( i)

(ii)

g(x) = (x-1)

( x-1) =0

x=1

p (1) = (1)³+a(1)²+ b(1) +5

= 1+a+b +5

= 6+a+b.................... (ii)

Now take eqn. (i)

4+ a - b = 0

a = b -4 ........................(iii)

Now put the value of a which we get in equation (iii) ,

From equation (ii) ,

6+a+b =0

6+ (b - 4 ) + b = 0

6+b - 4 + b =0

2b + 2 =0

2b = -2

b = -2/2

b = -1

take equation (iii)

a = b - 4 .

a = -1 -4

a = -5