If the gcd of x^2+10x+(p+6) and x^2+(p/3)x+8 is x+4
Answers
Given: The gcd of x^2+10x+(p+6) and x^2+(p/3)x+8 is x+4.
To find: The value of p?
Solution:
- Now we have given that gcd of x^2+10x+(p+6) and x^2+(p/3)x+8 is x+4. It means that x+4 is the common factor of both the given polynomial.
x + 4 = 0
x = -4
- Now we have polynomial equation which will be equal to zero.
x^2+10x+(p+6) = 0
(-4)^2 + 10(-4) + p + 6 = 0
16 - 40 + 6 + p = 0
p = 40 - 22
p = 18
x^2+(p/3)x+8 = 0
(-4)^2 -4p/3 + 8 = 0
16 + 8 = 4p/3
24(3)/4 = p
p = 18
Answer:
So the value of p is 18.
Answer:
Given: The gcd of x^2+10x+(p+6) and x^2+(p/3)x+8 is x+4.
To find: The value of p?
Solution:
Now we have given that gcd of x^2+10x+(p+6) and x^2+(p/3)x+8 is x+4. It means that x+4 is the common factor of both the given polynomial.
x + 4 = 0
x = -4
Now we have polynomial equation which will be equal to zero.
x^2+10x+(p+6) = 0
(-4)^2 + 10(-4) + p + 6 = 0
16 - 40 + 6 + p = 0
p = 40 - 22
p = 18
x^2+(p/3)x+8 = 0
(-4)^2 -4p/3 + 8 = 0
16 + 8 = 4p/3
24(3)/4 = p
p = 18
Answer:
So the value of p is 18.
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