CA Foundation · Quantitative Aptitude · Equations
What is the nature of the roots of the equation 2x² − 5x + 4 = 0?
The roots are complex, with no real roots. The discriminant of 2x² − 5x + 4 = 0 is 25 − 32 = −7, which is negative, and a quadratic with a negative discriminant has no real solutions.
- AReal and equal
- BReal and unequal
- CComplex (no real roots)Correct
- DRational and unequal
Explanation
Discriminant = b² − 4ac = 25 − 4(2)(4) = 25 − 32 = −7. Since it is negative, the equation has no real roots. Choosing 'real and unequal' comes from wrongly calculating the discriminant as positive, e.g. by ignoring the sign of 4ac.
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