Find the value of p and q if
( x - 1) and ( x + 2) are the factors of x3+ 3x2 -2px + q
Answers
Step-by-step explanation:
let f(x) = x³+3x²-2px+q. is given polynomial
since x-1 is a factor of f(x)*=> x-1=0=> x=1
=> f(1) should be zero
=> 1³+3×1³-2p×1+q= 0
=> 2p-q = 4.........................(1)
again, x+2 is a factor of. f(x) => x+2= 0=> x = -2
=> f(-2) should be zero.
=> (-2)³+3×(-2)²-2p(-2)+q = 0
=> -8+12+4p+q=0
=> 4p+q = -4.......................(2)
adding (1) and (2)
=> 6p = 0
=> p=0
putting p= 0 in (1)
4×0-q = 4
=> -q =4
=> q = -4
therefore, p = 0 , q = -4
Answer:
let f(x) = x³+3x²-2px+q. is given polynomial
since x-1 is a factor of f(x)*=> x-1=0=> x=1
=> f(1) should be zero
=> 1³+3×1³-2p×1+q= 0
=> 2p-q = 4.........................(1)
again, x+2 is a factor of. f(x) => x+2= 0=> x = -2
=> f(-2) should be zero.
=> (-2)³+3×(-2)²-2p(-2)+q = 0
=> -8+12+4p+q=0
=> 4p+q = -4.......................(2)
adding (1) and (2)
=> 6p = 0
=> p=0
putting p= 0 in (1)
4×0-q = 4
=> -q =4
=> q = -4
therefore, p = 0 , q = -4
Step-by-step explanation: