Question

If alpha and beta are the zeros of the quadratic polynomial x square minus k + 6 into x + 2 (2 k - 1), find the value of k so that alpha + beta equal to one by two you into alpha beta

Answer 1

Answer:

The value of k is 7

Step-by-step explanation:

Given:

$\alpha\:and\:\beta$ are zeros of $x^2-(k+6)x+2(2k-1)$

Then,

Sum of zeros:

$\alpha+\beta=\frac{-b}{a}$

$\alpha+\beta=\frac{k+6}{1}$

$\implies\:\alpha+\beta=k+6$

Product of zeros:

$\alpha\:\beta=\frac{c}{a}$

$\alpha\:\beta=\frac{2(2k-1)}{1}$

$\implies\:\alpha\:\beta=2(2k-1)$

Given:

$\alpha+\beta=\frac{1}{2}*\alpha\:\beta$

$\implies\:k+6=\frac{1}{2}*2(2k-1)$

$\implies\:k+6=2k-1$

$\implies\:1+6=2k-k$

$\implies\:k=7$

Answer 2

Answer:

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