Saved Bookmarks
| 1. |
Natue of root formula |
| Answer» The nature of the roots depends on the value of b2\xa0– 4ac. bx2\xa0– 4ac is called the\xa0discriminant\xa0of the quadratic equation ax2\xa0+ bx + c = 0 and is generally, denoted by D.∴\xa0D = b2\xa0– 4acIf D > 0, i..e., b2\xa0– 4ac > 0, i.e., b2 – 4ac is positive; the roots are\xa0real and unequal. Also,(i) If b2\xa0– 4ac is a perfect square, the roots are\xa0rational and unequal.(ii) If b2\xa0– 4ac is positive but not perfect square, the roots are\xa0irrational and unequal.If D = 0, i.e., b2\xa0– 4ac = 0; the roots are\xa0real and equal.If D < 0, i.e., b2 – 4ac < 0; i.e., b2\xa0– 4ac\xa0is negative; the roots are not real, i.e., the roots are\xa0imaginary. | |