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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?

bh , 5 Years ago
Grade 10
anser 2 Answers
Arun

Last Activity: 5 Years ago

 
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.

Vikas TU

Last Activity: 5 Years ago

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
Apply quadratic equation formula 
x = ± 3 ± sqrt(2) 
Which is irrational number.
Good Luck 

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