Question

For the cubic polynomial P (x)= x3-10x2+31x-30 the sum of the product of the zero taken two a time (-31,30,31)​

Answer 1

Step-by-step explanation:

Let the roots of given equation x

3

+kx

2

+31x−30=0 is p,q,r

by given condition,

p×q=15

Relation betwen roots and coefficients are

Product of the roots=

a

−d

∴p×q×r=

a

−d

=

1

−(−30)

=30

15r=30

r=2,

Sum of products of the roots taken two at a time=

a

c

∴p×q+p×r+q×r=

a

c

=

1

31

=31

15+r(p+q)=31

r(p+q)=16

p+q=16/2=8 and also

pq=15

So p+q+r=

a

−b

=

1

−k

=−k

(p+q)+r=−k

8+2=−k

k=−10