Math, asked by ushachokkakula, 8 months ago

find the values of the contants a and b if (x-2) and (x+3) are both factors of the expression x^3+ax^2+bx-12​

Answers

Answered by vishvraj0611
7

Answer:

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Step-by-step explanation:

Expression x3 + ax2 + bx – 12

(x – 2) is a factor i.e., at   x = 2 the remainder will be zero

⇒ (2)3 + a(2)2 + b(2) – 12 = 0

⇒ 8 + 4a + 2b – 12 = 0

⇒ 4a + 2b = 4

⇒ 2a + b = 2     ….(i)              

When  x + 3 is a factor  i.e.,   at  x = - 3 the remainder will be zero.

⇒ (- 3)3 + a(- 3)2 + b(- 3) – 12 = 0

⇒ - 27 + 9a – 3b – 12 = 0

⇒ 9a – 3b = 39

⇒ 3a – b = 13        ......(ii)

Solving (i) and (ii) simultaneously

2a + b = 2

By adding      3a – b = 13

5a = 15

a = 3

Substituting the value of a in the equation (i)

⇒ 2 × 3 + b = 2

⇒ 6 + b = 2

⇒ b = 2 – 6 = - 4

⇒ a = 3, b = - 4

Answered by prathamtyagi7009
2

Answer:

Step-by-step explanation:

Expression x3 + ax2 + bx – 12

(x – 2) is a factor i.e., at   x = 2 the remainder will be zero

⇒ (2)3 + a(2)2 + b(2) – 12 = 0

⇒ 8 + 4a + 2b – 12 = 0

⇒ 4a + 2b = 4

⇒ 2a + b = 2     ….(i)            

When  x + 3 is a factor  i.e.,   at  x = - 3 the remainder will be zero.

⇒ (- 3)3 + a(- 3)2 + b(- 3) – 12 = 0

⇒ - 27 + 9a – 3b – 12 = 0

⇒ 9a – 3b = 39

⇒ 3a – b = 13        ......(ii)

Solving (i) and (ii) simultaneously

2a + b = 2

By adding      3a – b = 13

5a = 15

a = 3

Substituting the value of a in the equation (i)

⇒ 2 × 3 + b = 2

⇒ 6 + b = 2

⇒ b = 2 – 6 = - 4

⇒ a = 3, b = - 4

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