CA Foundation · Quantitative Aptitude · Equations
What is the nature of the roots of the equation 2x² − 4x + 5 = 0?
The roots are complex, not real. The discriminant is (−4)² − 4(2)(5) = 16 − 40 = −24, which is negative. When the discriminant of a quadratic is below zero, no real roots exist, so the roots are a pair of complex conjugates.
- AReal, distinct and rational
- BReal and equal
- CReal, distinct and irrational
- DComplex (not real)Correct
Explanation
Discriminant D = b² − 4ac = 16 − 40 = −24, which is negative. A negative discriminant means the roots are not real. Option 'real and equal' would need D = 0, and the rational/irrational options need D > 0.
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