Find the value of P for which (x+1) is a factor
of ( x ⁴+(p-3)x³-(3p-5)+x²+(3p-9)x+6.
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Given
Find the value of P for which (x+1) is a factor
of ( x ⁴+(p-3)x³-(3p-5)+x²+(3p-9)x+6)
To find
Find the value of p
Solution
=> x + 1 = 0
=> x = -1
Putting the value of x
=> x⁴ + (p-3)x³ - (3p-5) + x² + (3p-9)x + 6 = 0
=> (-1)⁴ + (p-3)(-1)³ - (3p-5) + (-1)²+ (3p-9)(-1) +6=0
=> 1 + (p-3)(-1) - 3p + 5 + 1 - 3p + 9 = 0
=> 1 - p + 3 - 3p + 6 - 3p + 9 = 0
=> -p - 3p - 3p + 1 + 3 + 6 + 9 = 0
=> -7p + 19 = 0
=> 19 = 7p
=> p = 19/7
Hence, the value of p is 19/7
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