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alpha,beta are zeroes of a quadratic polynomial x^2 - (k + 6)x + 2(2k - 1). Find the value of k if alpha + beta = 1/2alphabeta​

Answer»

Question:-

ALPHA,BETA are zeroes of a quadratic polynomial x^2 - (k + 6)x + 2(2k - 1). FIND the value of k if alpha + beta = 1/2alphabeta.

ANSWER:-

Here is your answer,

x^2 -(k+6)x + 2(2k-1)=0

Sum of zeroes = -b\/a

Alpha + beta = -[-(k+6)]\/1

=-(k+6)

Product of zeroes= c\/a

Alpha x beta = 2(2k-1)\/1

= 2(2k-1)

ACCORDING to the question,

Alpha + beta = 1\/2 x alpha x beta

(k+6)=1\/2 x 2(2k-1)

k+6=2k-1

2k-k=6+1

k=7

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