Question

If alpha , beta are the zeroes of the quadratic polynomial f(x) = x2 -(k+6)x+ 2(2k-1), find the value of k so that alpha + beta =1/2 alpha beta

Answer 1

Hey dude!!

Here's your answer

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f ( x ) = x^2 - ( k + 6 ) x + 2 ( 2k - 1 )

Let's , a = 1 , b = - ( k + 6 ) , c = 2 ( 2k - 1 )

If , alpha and beta are the zeros of the quadratic polynomial

Then , alpha + beta = - { - ( k + 6 ) } / 1 = ( k + 6 )

And , alpha × beta = 2 ( 2k - 1 ) / 1 = ( 4k - 2 )

Here , alpha + beta = 1 / 2 alpha × beta

So now ,

( k + 6 ) = 1 / 2 × ( 4k - 2 )

4k - 2 = 2k + 12

4k - 2k = 12 + 2

2k = 14

k = 14 / 2

k = 7
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The value of k is 7 .

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Hope it helps you dear!! :)