Question

If the zeroes of the polynomial x3 - 9x2 + 18 are a-b,a,a+b,find a and b

Answer 1

I hope it help you please mark me in brain list

Answer 2

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

or, 3a  = -b/a

or, 3a = -(-9)/1

or, 3a = 9

or, a = 3

sum and product of roots = c/a

⇒ a(a+b) +(a+b)(a-b) + a(a-b)

or, a² +ba + a² -b² + a² -ab

or, 3² +3b + 3² -b² + 3² - 3b

or, 9 + 9 -b² +9 = c/a

or, 27 - b² = c/a

or, 27 -b² = 0/a

or, 27 -b² = 0

or, b² = 27

⇒ b² = 3*9

or, b = 3√3

∴ The value of 'a' = 3 and 'b' = 3√3