how important is the discriminant in determining the nature of roots?
Answers
This is the expression under the square root in the quadratic formula. The discriminant determines the nature of the roots of a quadratic equation. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.
Given : Discriminant
To Find : relation with nature of root
Solution:
Quadratic Equation
ax² + bx + c = 0
Discriminant denoted by D
D = b² - 4ac
D = 0
Hence equation has real and equal roots
D > 0 real and unequal roots
D < 0 roots are imaginary
Hence discriminant in very important in determining the nature of roots
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