The equation $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has which type of roots, when $a \neq b$ .

Two distinct real roots

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No real roots

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Two equal roots

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Two real roots

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Solution

The correct option is B No real roots
$D = [2 (a + b)]^{2} - 4 [2 (a^{2} + b^{2})] = a^{2} + b^{2} + 2 a b - 2 a^{2} - 2 b^{2}$
$= - (a - b)^{2}$ which is $\leq 0 ∴ D \leq 0 ∴$ no real roots

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The equation 2(a2+b2)x2+2(a+b)x+1=0 has which type of roots, when a≠b.

The correct option is B No real rootsD=[2(a+b)]2−4[2(a2+b2)]=a2+b2+2ab−2a2−2b2=−(a−b)2 which is ≤0∴D≤0∴ no real roots

The equation $2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$ has which type of roots, when $a \neq b$ .

The correct option is B No real roots
$D = [2 (a + b)]^{2} - 4 [2 (a^{2} + b^{2})] = a^{2} + b^{2} + 2 a b - 2 a^{2} - 2 b^{2}$
$= - (a - b)^{2}$ which is $\leq 0 ∴ D \leq 0 ∴$ no real roots