Discuss the nature of the roots of the equation: $\displaystyle 2(a^{2}+b^{2})x^{2}+2(a+b)x+1=0$

The nature of the roots is determined by the discriminant D = b^2 - 4ac. Substituting the coefficients from the equation yields D = [2(a+b)]^2 - 4 * 2(a^2+b^2) * 1, which simplifies to 4a^2 + 8ab + 4b^2 - 8a^2 - 8b^2 and results in -4(a-b)^2. Because the square of any real number is zero or positive, multiplying by -4 ensures the discriminant is always zero or negative, meaning the roots are imaginary and in conjugate pair.

• Thanks
• Wrong explanation