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First let's consider the standard quadratic equation
We know the solution to this equation is given by,
where is known as the determinant which determines the nature of the roots of the equation.
Since the square root of discriminant is included for the solution as in the equation,
- to get real roots, the value of discriminant should be non - negative.
- to get rational roots, the discriminant should be in such a way that it can be expressed as a square of a real number.
Here we're given the equation,
The discriminant is,
Here we see that the discriminant is expressed as a square of a real number, since a, b, c are real numbers. Also it is non - negative.
Thus we can say that the roots of the equation are rational, and the roots are,
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