Question

Verify that 1,3 and 4 are the zeroes of the cubic and polynomial P (X) = X cub - 8X square + 19x + 18 and then verify the relationship between the Zeroes and the coefficients.

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Answer 1

Step-by-step explanation:

p (x)= x³ - 8x² +19x +18

and the zeroes are 1,3 and 4

Verifying the zeros,

when x=1

p(1) = 1³-8(1)²+19(1)+18

p( 1 )= 1-8 +19 +18

p(1)= 30

when x= 3

p( 3 )= (3)³-8(3)²+19(3)+18

p(3) = 27 -72+57+18

p(3)= 30

when x=4

p(4) = (4)³-8(4)²+19(4)+18

p(4)= 30

now verify te relation b/w zeroes

p (x)= x³ - 8x² +19x +18

here a= 1 , b= -8 , c=19 , d= 18

and zeroes m= 1 ,n= 3 ,o= 4

m+n+o

= 1+3+4

= 8

8= -b/a

now

mn+ no+ on

(1)(3)+(3)(4)+(4)1

= 19

19=c/a

also n×m×o

(1)×(3)×(4)

12 doesn't equal to d/a

thus the relation is not verified

Answer 2

I hope it's clear to you

thank you.