How do I find value of k so that zeroes

esclaufitbzv

esclaufitbzv

Answered question

2022-03-02

How do I find value of k so that zeroes of polynomial
n3+12n2+39n+k
are in arithmetic progression?

Answer & Explanation

suable9w4

suable9w4

Beginner2022-03-03Added 4 answers

Step 1
Lets assume roots/zeros of the polynomial are rd, r and r+d
From the given polynomial the sum of the roots is 12
According to our assumption the sum is 3r
So, 3r=12 or r=4
Now F(n)=n3+12n2+39n+k has a root -4, so F(4)=0
This gives k=28
If you want to find the roots:
From the given polynomial the product of the roots is k or 28
According to our assumption the product of the roots is 4d264
So, 4d264=28 or d=±3
Thus the roots are -1, -4 and -7
Yosef Krause

Yosef Krause

Beginner2022-03-04Added 8 answers

Step 1
n3+12n2+39n+k=0 has roots xd, x, x+d
sum of roots is 12=3x
so x=4 is a root
So 43+12×42×+39×(4)+k=0
Thus, k=28

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