Question

For the polynomial f(x) = x3 + ax2 + bx + C, the
sum of two zeroes is 0, then find the relation
between a, b and c.​

Answer 1

Answer:

Step-by-step explanation:

sum of two roots is zero

sum of roots is-b/a for ax3 + bx2 + cx + d

here sum is -a

so third root is -a

so f(-a)=0

-a^3+a^3-ab+c=0

-ab+c=0

c=ab

that's the relation

Answer 2

ab = c is the relation between a, b and c if for polynomial f(x) = x³ + ax² + bx + c  , sum of two zeroes is 0

Given :

• Polynomial function

• f(x) = x³ + ax² + bx + c
• sum of two zeroes is 0

To Find:

• The relation between a, b and c

Solution:

Step 1:

Assume that roots of f(x) = x³ + ax² + bx + c    are

m , - m and n

As sum of m and - m = 0

Step 2:

Sum of roots  = - a

m + (-m) + n = - a

=> n = - a

Hence one of the root is - a

Step 3:

As -a is one of the root hence f(-a) = 0

(-a)³ + a(-a)² + b(-a) + c = 0

=> -a³ + a³ -ab + c = 0

=> -ab + c = 0

=> ab = c

ab = c is the relation between a, b and c if for polynomial f(x) = x³ + ax² + bx + c  , sum of two zeroes is 0