Question

The roots of the equation x²+bx+c=0are equal if ?

Answer 1

Answer:

The roots of the quadratic equation,

p(x)=ax²+bx+c=0

are numerically exactly equal to each other only if the discriminant of the polynomial is equal to 0.

i.e., D=0=b²–4ac

=>b²=4ac or b=2√(ac)

This is the required condition so as for the roots of the given quadratic equation to be equal

Answer 2

Answer:

A quadratic equation is the equation which has the degree 2. It is in the form ax²+bx+c=0.

If x is the root of the equation then the formula is,

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

As the question has asked for the condition for which the roots of the equation x²+bx+c=0 so we need to find the discriminant (D) ;

D = b²-4ac [formula of discriminant]

Properties of the discriminant are :

• b²-4ac= 0 [equal and rational roots]
• b²-4ac >0 [distinct real roots]
• b²-4ac<0 [imaginary roots]

So the condition b²-4ac=0 satisfy our answer for equal roots.

Therefore,

b²-4ac = 0

b²-4c = 0

b²= 4c

Thus if b²=4ac then this satisfy for equal roots for the quadratic equation.