Prove that the roots of the equation 2kx 2 + 5x k = 0 are real

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Prove that the roots of the equation 2kx² + 5x − k = 0 are real and distinct for all real values of k.

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Answer To prove that the roots of the equation 2kx 2 5x k 0 are real and distinct for all real values of k we need to show that the discriminant of the quadratic equation is always positive which means that the equation has two distinct real roots The discriminant of a quadratic equation ax 2 bx c 0 is given by b 2 4ac So the discriminant of the given equation is 5 2 42kk 25 8k 2 To prove that the discriminant is always positive for all real values of k we can show that 25 8k 2 0 for all real values of k Lets start by assuming that 25 8k 2 0 for some real value ...View the full answer

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Rathnakaran S R

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