Natue of root formula
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Gaurav Seth 5 years, 1 month ago
The nature of the roots depends on the value of b2 – 4ac. bx2 – 4ac is called the discriminant of the quadratic equation ax2 + bx + c = 0 and is generally, denoted by D.
∴ D = b2 – 4ac
If D > 0, i..e., b2 – 4ac > 0, i.e., b2 – 4ac is positive; the roots are real and unequal. Also,
(i) If b2 – 4ac is a perfect square, the roots are rational and unequal.
(ii) If b2 – 4ac is positive but not perfect square, the roots are irrational and unequal.
If D = 0, i.e., b2 – 4ac = 0; the roots are real and equal.
If D < 0, i.e., b2 – 4ac < 0; i.e., b2 – 4ac is negative; the roots are not real, i.e., the roots are imaginary.
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