Question

if alpha and beta are the zeroes of polynomial 6x²+5x+k such that alpha-beta=1/6.Find the value of k
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Answer 1

Answer:

1

Step-by-step explanation:

Given polynomial : 6x² + 5x + k

Comparing with ax² + bx + c we get,

• a = 6
• b = 5
• c = k

α, β are the zeroes of the polynomial

Sum of zeroes = α + β = - b / a = - 5 / 6

Product of zeroes = αβ = c / a = k / 6

Given :

α - β = 1/6

Using algebraic identity ( α + β )² - ( α - β )² = 4αβ

=> ( - 5 / 6 )² - ( 1 / 6 )² = 4( k/6 )

=> 25/36 - 1/36 = 4k/6

=> ( 25 - 1 ) / 36 = 4k/6

=> 24 / 36 = 4k/6

=> 24/36 × 6 = 4k

=> 24/6 = 4k

=> 4 = 4k

=> 1 = k

=> k = 1

Therefore the value of x is 1.