Nature of Roots of Quadratic Polynomial
Nature of Roots of Quadratic Polynomial
Nature of Roots of Quadratic Polynomial:
The Value of Discriminant decides the nature of roots of a quadratic Polynomial.
Case 1: If , then the roots are real and equal
Case 2: If , then the roots are real and unequal.
Case 3: If , then the roots are imaginary
Example: Without solving the equation identify the nature of roots
Solution: Comparing the equation with the standard form
a = 2, b = 5 and c = 5, Then
As the discriminant is less than zero so the roots are imaginary
Example: Find the value of k for which the equation has real and equal roots
Solution: Comparing the equation with the standard form
a = 1, b = -2(1+3k) and c = 7(3+2k), Then
As the roots are real and equal, so D = 0
The number of real roots of equation: | |||
| Right Option : C | |||
| View Explanation | |||
If the quadratic equation | |||
| Right Option : A | |||
| View Explanation | |||
Find the nature of the roots of | |||
| Right Option : C | |||
| View Explanation | |||
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