Question

if the zeros of polynomial x^3- 2x^2+x+1 are (a-b), a, (a+b). Then find the values of a and b.​

Answer 1

In a cubic equation ax³ + bx² + cx + d,

Sum of roots = -b/a

Product of roots = -d/a

Sum of roots = (a+b + a + a-b) = 3a = -(-2)

∴ a = 2/3

(a - b)(a)(a + b) = -1

(2/3)(4/9 - b²) = -1                           ------ { using (a+b)(a-b) = a² - b² }

b² = 4/9 + 3/2 = 35/18

∴ b = √(35/18)

Answer 2

Answer:

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Step-by-step explanation:

In a cubic equation ax³ + bx² + cx + d,

Sum of roots = -b/a

Product of roots = -d/a

Sum of roots = (a+b + a + a-b) = 3a = -(-2)

∴ a = 2/3

(a - b)(a)(a + b) = -1

(2/3)(4/9 - b²) = -1                           ------ { using (a+b)(a-b) = a² - b² }

b² = 4/9 + 3/2 = 35/18

∴ b = √(35/18)