Question

find the rational roots for the polynomial 4x^3+ 20x^-23x+6by newton's method of divisors ​

Answer 1

Answer:

MATHS

Solve the equations:

4x

3

+20x

2

−23x+6=0, two of the roots being equal.

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ANSWER

4x

3

+20x

2

−23x+6=0

Let the roots be a,a,b

∑x=a+a+b=−

4

20

=−5

2a+b=−5

⇒b=−5−2a....(i)

∑xy=a(a)+a(b)+b(a)=

4

−23

a

2

+2ab=

4

−23

substituting b from (i)

4a

2

+8ab+23=0

4a

2

+8a(−5−2a)+23=0

4a

2

−40a−16a

2

+23=0

12a

2

+40a−23=0

12a

2

−6a+46a−23=0

⇒a=

2

1

,−

6

23

substituting a in (i)

⇒b=−6,−

3

8

∑xyz=a

2

b=−

4

6

=−

2

3

Product of roots do not satisfy a=−

3

8

So the roots of the equation are

2

1

,

2

1

,−