A quadratic equation in the form of
Β a xΒ² + b x + c=0, has
Discriminant = D= bΒ²- 4 ac
x = [tex]\frac{-b \pm \sqrt{D}}{2a}[/tex]
Now coming to roots of a quadratic equation
1. Dβ₯0, both the roots are real i.e both of them may be rational or both of them may be rational.
2. D=0, both the roots are real and equal.
3. D< 0, both the roots are imaginary.
So, out of following options given,
Option A, is not true,
zero, because the discriminant is negative.(It is a true statement if you are talking about real roots but if we consider imaginary roots also then this statement becomes false.) .In the question it is given that Β that roots are in radical form that's why this option is incorrect.
. Option B is not true because if Discriminant is not a perfect square then also the quadratic function has two real either rational or irrational roots.
Third option is completely false , it is incorrect statement.[one, because the negative and the minus cancel each other]
Fourth option is true because , in the answer it has been written that the roots are in simplest radical form , The value of D should always be greater than zero,then we look at Β± symbol .Then there are two possible real roots.
The value of D should always be greater than zero, then we look at the Β± symbol. Then there are two possible real roots.
The equation which has the highest power or degree is 2 called the quadratic equation.
The general form of the quadratic equation is given by;
[tex]\rm ax^2+bx+c=0[/tex]
Where; a, b, and c are the constants and a can not be zero.
The discrimination for the quadratic equation is given by;
[tex]\rm Discriminate = b^2-4ac[/tex]
Hence, the value of D should always be greater than zero, then we look at the Β± symbol. Then there are two possible real roots.
To know more about the Quadratic equation click the link given below.
https://brainly.com/question/3751209
