Dual answers for polynomial question (1 Viewer)

[sinophile]

I keep getting two answers for this polynomial question, one which is in the answers of the textbook, and another where b=14/5 and a=392/25, and seems to be correct but isn't in the textbook answers. Am I right, or is there something im doing wrong?

The question is from Fitzpatrick: "if 5x^(2)-6x-56 and 3x^(2)-14x+a have a common factor (x+b), find the values of a and b."

 

[Trebla]

I keep getting two answers for this polynomial question, one which is in the answers of the textbook, and another where b=14/5 and a=392/25, and seems to be correct but isn't in the textbook answers. Am I right, or is there something im doing wrong?

The question is from Fitzpatrick: "if 5x^(2)-6x-56 and 3x^(2)-14x+a have a common factor (x+b), find the values of a and b."

Let P(x) = 5x² - 6x - 56 and Q(x) = 3x² - 14x + a
We're given that P(-b) = Q(-b) = 0
5b² + 6b - 56 = 0
=> (b + 4)(5b - 14) = 0
b = - 4, 14/5
Also,
3b² + 14b + a = 0
=> a = - 14b - 3b²
When b = - 4, a = 8
When b = 14/5, a = -1568/25

 

[sinophile]

So thereARE two answers?

 

[jchoi]

I keep getting two answers for this polynomial question, one which is in the answers of the textbook, and another where b=14/5 and a=392/25, and seems to be correct but isn't in the textbook answers. Am I right, or is there something im doing wrong?

The question is from Fitzpatrick: "if 5x^(2)-6x-56 and 3x^(2)-14x+a have a common factor (x+b), find the values of a and b."

Yes