Write the nature of the quadratic equation ax2+bx+c=0 if. (1) b2-4ac =0 (2) b2-4ac>0
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The nature of the quadratic equation ax^2+bx+c=0 if (1) b^2-4ac=0 is, the roots of a quadratic equation are real and equal, and for (1)b^2-4ac>0 is, the roots of a quadratic equation are real and unequal.
- Given,
- The quadratic equation: ax^2+bx+c=0
- Conditions to check
- (1) b^2-4ac=0
- (2) b^2-4ac>0
- As we all know, a quadratic equation has 2 roots.
- where, a,b and c are real and rational numbers.
- is called as the determinant.
- This determinant defines the nature of the roots of a quadratic equation.
- (1)b^2-4ac=0
- when, a, b and c are real numbers, a≠0 and determinant is equal to zero, then the roots of a quadratic equation are real and equal.
- (2)b^2-4ac>0
- when, a, b and c are real numbers, a≠0 and determinant is positive, then the roots of a quadratic equation are real and unequal.
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