1.

27. if a and B are the zeros of the quadratic polynomial f(x) = 6x2 + x - 2, find the value of α/β+β/α​

Answer»

Answer:-

Given Polynomial: 6x² + x - 2

Let a = 6 ; b = 1 ; c = - 2

We know that,

Sum of the zeroes = - b/a

→ α + β = - 1/6 -- equation (1)

Product of the zeroes = c/a

→ αβ = - 2/6

→ αβ = - 1/3 -- equation (2)

We have to find:

α/β+β/α = ?

Taking LCM we get,

→ ( α² + β² ) / αβ

We know that,

(a + b)² = a² + b² + 2ab

→ (a + b)² - 2ab = a² + b²

→ (α + β)² - 2αβ = α² + β²

Hence,

→ [ (α + β)² - 2αβ ] / αβ

Putting the VALUES from equation (1) and (2) we get,

→ [ ( - 1/6)² - 2( - 1/3) ] / (- 1/3)

→ [ 1/36 + 2/3 ] / ( - 1/3)

→ [ (1 + 24) / 36 ] * ( - 3)

→ 25 / 36 * ( - 3)

→ - 25 / 12

Hence, the value of α/β + β/α is - 25/12.


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