Question

If the zeroes of the polynomial x^3-9x^2+18 are a-b a a+b find a and b

Answer 1

Answer:

Given:

polynomial x³ -9x² + 18

and zeros, a-b,a,a+b,find a and b

To find:

The values of 'a' and 'b'.

Pre-requisite Knowledge:

sum of roots = α+β+γ = -b/a

sum and product of roots = c/a

where the polynomial is ax³ + bx² + cx + d = 0

Solving Question:

zeros, a-b,a,a+b,find a and b

⇒ (a-b)+(a+b)+a =  -b/a

3a  = -b/a

3a = -(-9)/1

3a = 9

a=9/3

a = 3

sum and product of roots = c/a

⇒ a(a+b) +(a+b)(a-b) + a(a-b)

a² +ba + a² -b² + a² -ab

3² +3b + 3² -b² + 3² - 3b

9 + 9 -b² +9 = c/a

27 - b² = c/a

27 -b² = 0/a

27 -b² = 0

b² = 27

⇒ b² = 3*9

b = 3√3

∴ The value of 'a' = 3 and 'b' = 3√3