Question

PLZZ SOLVE THIS 》 If alpha and beta are the zeroes of the quadratic polynomial 6x^2+5x-1 then find a polynomial whose zeros are》
a) 1/alpha , 1/beta
b) alpha square , beta square
c) (2 alpha + 3beta) , (3alpha + 2beta)

Answer 1

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Answer 2

Answer:

(a) 5

(b) 37/36

(c) 4

Step-by-step explanation:

Given Quadratic equation is 6x² + 5x - 1

Here, a = 6, b = 5, c = -1.

α,β are the roots of the quadratic equation.

(i) Sum of roots:

⇒ α + β = -b/a

            = -5/6

(ii) Product of roots:

⇒ αβ = c/a

         = -1/6.

Now,

(a) (1/α) + (1/β)

= (α + β)/αβ

= (-5/6) * -6

= 5.

(b) α² + β²

= (α + β)² - 2αβ

= (-5/6)² - 2(-1/6)

= (25/36) + 1/3

= (25 + 12)/36

= 37/36.

(c) (2α + 3β)(3α + 2β)

= 2α(3α + 2β) + 3β(3α + 2β)

= 6α² + 13αβ + 6β²

= 6[α² + β²] + 13αβ

= 6[37/36] + 13(-1/6)

= 37/6 - 13/6

= (37 - 13)/6

= 24/6

= 4.

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