A polynomial in x whose roots are 4 3 and -3 5 ... - JAMB Mathematics 2009 Question
A polynomial in x whose roots are 4/3 and -3/5 is
A
15x2 - 11x – 12
B
15x2 + 11x – 12
C
12x2 - x – 12
D
12x2 + 11x – 15
correct option: a
If 4/3 and -3/5 are roots of a polynomial
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
∴3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x – 20x – 12 = 0 By expansion
15x2 - 11x – 12 = 0
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