1.

(X+2)&(x-3)are factors of xcube +ax+be. Find the values of a and b.Also find the remaining factors

Answer»

Hello Mate!

Polynomial we have is p(x) = x³ + ax + b

SINCE two of the FACTORS are ( x + 2 ) and ( x - 3 ) so respective value of x = - 2 and 3.

Keeping values if x we get,

p(x) = -2³ + a(-2) + b

0 = - 8 - 2a + b

8 = - 2a + b or - 8 = 2a - b __(1)

p(x) = 3³ + a(3) + b

- 27 = 3a + b __(2)

On adding (1) and (2)

- 35 = 5a

- 7 = a

Keeping value of a in equation (1) we get

- 8 = 2(-7) -  b

- 8 + 14 = - b

- 6 = b

So, p(x) = x³ + ax + b

p(x) = x³ + 0x² - 7x - 6

Please REFER to attatchment above!

Hence other factor is ( x + 1 ).

So zeros if polynomial are x = - 2, + 3 and - 1.

Have marvelous future ahead!


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