1) if x+2 and x+3 are factor of the polynomial xpower 4+ 5xcube +15x +18 find the other factor
2) find the value of a and b such that the polynomials xcube +10xsquare +ax+b is exactly divisible by x-1 and x+2 .
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Answered by
2
2) a = 7 and b = -18
i think there will be some mistake in the first question
i think there will be some mistake in the first question
Answered by
3
The polynomial was incorrectly given.
P(x) = x⁴ + 5 x³ + 15 x + 18
x+2 and x+3 are roots. P(-2 ) = 0 P(-3) = 0
+ 16 - 40 -30 + 18 ≠ 0. so x+2 is not a factor of given polynomial.
there is some thing wrong with the polynomial given.
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2)
P(x) = x³ + 10 x² + a x + b
divisible by x - 1 and x+2
P(1) = 0 => 1 + 10 + a + b = 0 => a + b = -11
p(-2) = 0 => -8 + 40 -2 a + b = 0 => -2 a + b = -32
solving the equations we get: a = 7, b = -18
P(x) = x⁴ + 5 x³ + 15 x + 18
x+2 and x+3 are roots. P(-2 ) = 0 P(-3) = 0
+ 16 - 40 -30 + 18 ≠ 0. so x+2 is not a factor of given polynomial.
there is some thing wrong with the polynomial given.
===================================
2)
P(x) = x³ + 10 x² + a x + b
divisible by x - 1 and x+2
P(1) = 0 => 1 + 10 + a + b = 0 => a + b = -11
p(-2) = 0 => -8 + 40 -2 a + b = 0 => -2 a + b = -32
solving the equations we get: a = 7, b = -18
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