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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
Dear student As product of roots = 7hence 2k^2 – 1 = 7k^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
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 + 7Apply quadratic equation formula x = ± 3 ± sqrt(2) Which is irrational number.Good Luck
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