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Question
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:
2x2 - (3k + 1)x - k + 7 = 0.
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Solution
2x2 - (3k + 1)x - k + 7 = 0
Here,
a= 2,
b = -(3k + 1)
c = -k + 7
Sum of roots = `(-b)/a`
= `(3k + 1)/(2)`
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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