Question

If a and b are the zeros of polynomial 3x² - 2x -5 then find a/b+b/a

Answer 1

Step-by-step explanation:

Given polynomial is 3x² - 2x - 5.

To find: α/β + β/α

In the given polynomial a is 3, b is -2 and c is -5.

Sum of zeros = -b/a

α + β = -(-2)/3

α + β = 2/3

Product of zeros = c/a

α × β = c/a

α × β = -5/3

Now,

α/β + β/α = (α² + β²)/αβ

Substitute the values,

α/β + β/α = [(α + β)² - 2αβ]/αβ

α/β + β/α = [(2/3)² - 2(-5/3)]/(-5/3)

α/β + β/α = (4/9 + 10/3)/(-5/3)

α/β + β/α = [(4 + 30)/9]/(-5/3)

α/β + β/α = (34/9)/(-5/3)

α/β + β/α = 34/9 × (-3)/5

α/β + β/α = -34/15

Hence, the value of α/β + β/α is -34/15.

Answer 2

Answer:

(x-(a-b))(x-a)(x-(a+b))

= x^3 - 3ax^2 + (3a^2-b^2)x + ab^2-a^3

If that is identical to x^3-3x^2+x+1 then

-3a = -3

3a^2-b^2 = 1

ab^2-a^3 = 1

a=1 b=±√2