Question

If (x−2 ) (x−3) are the factors of x^3 + ax^2+ bx − 30 , find the values of a and b.

Answer 1

Answer:

a = - 10, b = 31

Step-by-step explanation:

Substituting value if x = 2 and 3 within the equation x³ + ax² + bx − 30 should result in zero.

When x = 2;

2³ + a*2² + b*2 - 30 = 0

=> 4a + 2b - 22 = 0

=> 2a  + b = 11 ------------- [1]

When x = 3;

3³ + a*3² + b*3- 30 = 0

=> 9a + 3b - 3 = 0

=> 3a  + b = 1        ------------- [2]

Subtract [1] from [2]

3a + b = 1

2a + b = 11

-     -       -

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a  = - 10

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Substitute value of a in [2]

3 * -10 + b = 1

=> -30 + b = 1

=> b = 31.