If discriminant is negative then the nature of roots is imaginary.
For a general quadratic equation, [tex]ax^2+bx+c=0[/tex]
the roots of the equation are [tex]\alpha=\frac{-b-\sqrt{b^2-4ac}}{2a}\ and\ \beta=\frac{-b+\sqrt{b^2-4ac}}{2a}[/tex]
Where, [tex]b^2-4ac[/tex] is known as discriminant.
If
Case i) [tex]b^2-4ac > 0[/tex]
then discriminant is positive and the roots α and β of the quadratic equation are real and unequal.
Case ii) [tex]b^2-4ac =0[/tex]
then discriminant is zero and the roots α and β of the quadratic equation are real and equal.
Case iii) [tex]b^2-4ac < 0[/tex]
then discriminant is negative and the roots α and β of the quadratic equation are unequal and not real, it means imaginary.
Case iv) [tex]b^2-4ac > 0[/tex] and perfect square
then discriminant is positive and perfect square and the roots α and β of the quadratic equation are real, rational and unequal.
Hence, if discriminant is negative then the nature of roots is imaginary.
To learn more about quadratic equations refer here
https://brainly.com/question/19776811
#SPJ4
