Question

Write the nature of the quadratic equation ax2+bx+c=0 if. (1) b2-4ac =0 (2) b2-4ac>0

Answer 1

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.
• $\alpha =\dfrac{-b-\sqrt{b^2-4ac} }{2a} , \beta =\dfrac{-b+\sqrt{b^2-4ac} }{2a}$
• where, a,b and c are real and rational numbers.
• $b^2-4ac$ 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 $\alpha ,\beta$ 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 $\alpha ,\beta$ are real and unequal.