# Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:

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asked Feb 16

Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following: ## 1 Answer

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answered Feb 16 by (-11,279 points)

(i) kx2 + 2x + 3k = 0

Here, a = k,  b = 2, and c = 3k

Sum of roots =  - b/a =  - 2/k

Product of roots = c/a

= 3k/k = 3

Sum of  roots  = Product of roots

-2/k = 3

⇒  3k = - 2

⇒ k = - 2/3

(ii) 2x2 – (3k + 1)x – k + 7 = 0

Here,   a = 2,

b =   -(3k + 1)

c =   - k + 7

Sum of roots = - b/a

= 3k + ½

Product of roots = c/a

=  - k + 7/2

Sum of  roots = Product of roots

3k + 1/2 =  - k + 7/2

6k + 2 =  - 2k + 14

8k = 12,  ⇒  k = 12/8

∴    k = 3/2

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