Question

What do you think is the importance of the expression in determining the nature of the roots of quadratic equation?

Answer 1

Answer:

We say this because the root of a negative number can't be any real number. ... Therefore for this equation, there are no real number solutions. Hence, the expression (b2 – 4ac) is called the discriminant of the quadratic equation ax2 + bx + c = 0. Its value determines the nature of roots as we shall see.

Step-by-step explanation:

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Answer 2

Answer:

b²-4ac

b²-4ac> 0  Real and unequal

b²-4ac=0 Real and equal

b²-4ac<0 No real roots(It has Imaginary roots)

Step-by-step explanation:

The roots of the equation ax²+bx+c=0 are given by

x=(-b±$\sqrt{b^{2}-4ac }$)/2a

If b²-4ac> we get two distinct real roots

x= $\frac{-b+\sqrt{b^{2}-4ac } }{2a}$  and  $\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

If b²-4ac=0, then the equation has two equal roots x=-b/2a

If b²-4ac<0, then  $\sqrt{b^{2}-4ac }$  is not a real number. There is no real root for the given quadratic equation.

The value of the expression b²-4ac discriminates the nature of the roots of ax²+bx+c=0 and so it is called the discriminant of the quadratic equation .