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Sum of N Terms of an AP

show that the...

Question

show that the equation $2 (m^{2} + n^{2}) x^{2} + 2 (m + n) x + 1 = 0$ has no real roots when $m \neq n$ .

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Solution

$2 (m^{2} + n^{2}) x^{2} + 2 (m + n) + 1 = 0$

$D = B^{2} - 4 A C$

$D = [2 (m + n)]^{2} - 4 \times 2 (m^{2} + n^{2})$

After solving you will get $D = - 4 (m - n)^{2}$

As $(m - n)^{2}$ is always positive

Hence, $D < 0$

The given equation has no real roots.

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