Question

Find k if the sum of zeroes of p(x) = x^2 - (k + 6)x + 2(2k-1) is half of their product

Answer 1

we have to find sum of zeroes and product of zeroes then according to question and solving the value of k will be 7

Answer 2

SOLUTION :  

Option (b) is correct : 7  

Given : x² - (k + 6)x + 2 (2k - 1) = 0

On comparing the given equation with ax² + bx + c = 0  

Here, a = 1 , b = - (k + 6) , c =  2 (2k - 1)

Sum of roots = - b/a

Sum of roots = - - (k + 6) /1

Sum of roots = k + 6  

Product of roots = c/a

Product of roots = 2 (2k - 1)

Product of roots = 4k - 2

Given : sum of roots = ½ Product of roots

k + 6 = ½ (4k - 2 )

2(k + 6) = 4k - 2

2k + 12 = 4k - 2

2k - 4k = - 2 - 12

-2k = - 14

2k = 14

k = 14/2  

k = 7

Hence, the value of k is 7 .

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