on dividing the polynomial x^3+2x^2+kx+7 by x-3, remainder comes out to be 25. Find quotient and the value of k. Also find the sum and product of zeroes of the quotient so obtained.
Answers
Answer:
The value of k is -9 and the quotient is
Sum of the zeroes of the quotient is -3-2=-5
Product of the zeroes of the quotient is (-3)(-2)=6
Explanation:
Given polynomial is
When the given polynomial is divided by x-3 we get the remainder 25
By Synthetic division we can solve this
Given the divisor x-3 therefore x-3 is a factor of given polynomial
So that 3_| 1 2 k 7
0 3 15 3(k+15)
______________________
1 5 k+5 7+3(k+15)
Given that the remainder is 25
so we have 7+3(k+15)=25
7+3(k)+3(15)=25
7+3k+45=25
3k=25-7-45
3k=-27
∴ k=-9
Now we have the quadratic equation as quotient
( here k=-9)
Therefore x+3 and x+2 are factors of the quotient
x+3=0 or x+2=0
x=-3 or x=-2 are zeroes of the quotient
Sum of the zeroes of the quotient is -3-2=-5
Product of the zeroes of the quotient is (-3)(-2)=6
Step-by-step explanation:
hope this was helpful
pls mark me as BRAINLIST