Question

Solve this math problem

Answer 1

Answer:

a = 0.2 , b = -7.4

Step-by-step explanation:

Given :

(x - 2) is a factor of the equation x³ + ax² + bx + 6 &

(x + 3) gives reminder 3 when the equation was divided by it,.

To Find :

The values of a & b,

Solution :

By dividing the equation by (x - 2) (1st picture) & (x + 3) (2nd picture)

We obtain 2 equations,

As the 1st & 2nd part of the answer is given in pictures below,

the 3rd part is here,.

⇒ 2a + b + 7 = 0 ...(i)

⇒ b - 3a + 8 = 0 ...(ii)

By subtracting (ii) from (i),

⇒ ( 2a + b + 7) - (b - 3a + 8) = 0 + 0

⇒ 2a + 3a + b - b + 7 - 8 = 0

⇒ 5a - 1 = 0 ⇒  a = $\frac{1}{5}$ = 0.2

By substituting value of a in (ii),

We get,

⇒ b - 3(0.2) + 8 = 0

⇒ b - 0.6 + 8 = 0

⇒ b + 7.4 = 0 ⇒ b = - 7.4

Answer 2

Answer:

p(x)=x^3(x raise to power 3) +ax^2 + bx+6

Since x-2 is a factor of this polynomial,2 is a zero of this polynomial.

When we put the value of 2 in x:

(2)^3 +a(2)^2+b(2)+6

=8+4a+2b+6

=14+4a +2b

4a+2b=-14(equation 1)

It is given that when this polynomial is divided by x+3 it gives a remainder 3.

By long division(photo attached ) the remainder comes out to be -12-3b.

Since remainder is equal to 3

-12-3b =3

-3b=3+12

-3b=15

b=-5.

Put this value of b in equation 1

4a+2(-5)=-14

4a=-14+10

4a=-4

a=-1.

Therefore,a=-1 and b=-5.