Two distinct real roots are there if the discriminant of quadratic equation is greater than zero.
What is quadratic equation ?
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
There are two different real roots when the discriminant is higher than 0. There is just one real root when the discriminant is equal to 0. There are exactly two unique imaginary roots when the discriminant is smaller than zero, but no real roots. In this instance, there are two actual roots.
We are aware that the discriminant of a quadratic equation can be used to determine the type of roots in the equation. There will be two real and separate roots to the equation if the discriminant is bigger than zero.
There will be a real root in the equation if the discriminant is zero. The equation will only have two complex roots rather than any real roots if the discriminant is smaller than zero.
The locations where an equation's curve intersects the x-axis can be used to define an equation's roots graphically.
Therefore, the curve crosses the x-axis twice if an equation has two roots. This graph is provided by;
quadratic equation of the kind discriminant;
ax^2 + bx + c = 0 is given by D = b^2 -4ac.
If D>0, the equation has 2 real and distinct roots. They are given by
[tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
If D=0, the equation has a real root, which is given by,
x = -b/2a
If D<0, the equation has complex roots.
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