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# for a given value of k the product of the solutions of x^2-3kx+2k^2-1=0 is 7. Are the roots rational, irrational, or imaginary

one year ago

Arun
25141 Points

Dear student

As product of roots = 7
hence 2k^2 – 1 = 7
k^2 = 4

k = ± 2

Now discriminant

9k^2 – 8k^2 + 4 = k^2 + 4 = 4 + 4 = 16 = positive and perfect square

Hence roots are rational
one year ago
Vikas TU
13786 Points

Dear student
Product of zeroes = 7
2k^2 -1 =7
2k^2= 8
k= 2 (Positive or negative)
So given equation x 2 – 3kx + 2k 2 – 1
becomes x 2 ± 6x + 7
x = ± 3 ± sqrt(2)
Which is irrational number.
Good Luck

one year ago
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