Math, asked by sofia123, 10 months ago

find the value of A and B such that the polynomial f of x is equal to 3 x cube + x square - 13 x + b is divisible by x square - 2 x minus 3​

Answers

Answered by TheBrainlyGirL001
2

⠀⠀⠀⠀ ☛ Solution ☚⠀ ⠀

⠀ ⠀

polynomial , x³ -ax² -13x + b has two factors ( x -1) and (x +3)

it means , x = 1 and -3 are the roots (zeros ) of x³ -ax² -13x + b...

so,

put x = 1 in polynomial ,.

  • (1)³ -a(1)² -13(1) + b = 0

  • 1 - a -13 + b = 0

  • -a + b = 12 ---------(1)

put x = -3

  • (-3)³ -a(-3)² -13(-3) + b = 0

  • -27 -9a +39 + b = 0

  • -9a + b = -12 --------(2)

subtract equation (1) and (2)

  • - a + b + 9a - b = 12 + 12

  • 8a = 24

  • a = 3

put a = 3 in equation (1)

  • b = 15

Therefore, the value of a is 3 and value of b is 15...⠀

Answered by amberpandey647
1

Answer:

polynomial , x³ -ax² -13x + b has two factors ( x -1) and (x +3)

it means , x = 1 and -3 are the roots (zeros ) of x³ -ax² -13x + b...

so,

put x = 1 in polynomial ,.

(1)³ -a(1)² -13(1) + b = 0

1 - a -13 + b = 0

-a + b = 12 ---------(1)

put x = -3

(-3)³ -a(-3)² -13(-3) + b = 0

-27 -9a +39 + b = 0

-9a + b = -12 --------(2)

subtract equation (1) and (2)

- a + b + 9a - b = 12 + 12

8a = 24

a = 3

put a = 3 in equation (1)

b = 15

Therefore, the value of a is 3 and value of b is 15...

Step-by-step explanation:

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