Question

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Answer 1

Polynomial ➡️ 3x² + (2k+1)x -(k+5)

$a = 3 \\ b = (2k + 1) \\ c = - (k + 5)$

We know ,

Sum of zeros = -b/a

Product of zeros = c/a

According to the question,

$2 \times \frac{ - b}{a} = \frac{c}{a} \\ = > 2 \times \frac{ - (2k + 1)}{3} = \frac{ - (k + 5)}{3} \\ = > 4k + 2 = k + 5 \\ = > 3k = 3 \\ = > k = \frac{3}{3} \\ = > k = 1$

Answer 2

Answer:

q.4

Hi ,

Let p( x ) = 3x² + 2kx + x - k - 5

= 3x² + ( 2k + 1 ) x - ( k + 5 )

compare p( x ) with ax² + bx + c

a = 3 , b = 2k + 1 , c = - ( k + 5 )

1 ) sum of the zeroes = - b / a

= - ( 2k + 1 ) / 3

2 ) product of the zeroes = c /a

= - ( k + 5 ) / 3

according to the problem given ,

- ( 2k + 1 ) / 3 = 1/2 [ - ( k + 5 ) / 3 ]

2 ( 2k + 1 ) = ( k + 5 )

4k + 2 = k + 5

4k - k = 5 - 2

3k = 3

k = 3/3

k = 1

I hope this helps you.

:)

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