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kaliprasad
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form quadratic equation $ax^2 +bx+c=0$ in parametric form such that a,b,c are integers in AP and it has got rational roots
kaliprasad said:form quadratic equation $ax^2 +bx+c=0$ in parametric form such that a,b,c are integers in AP and it has got rational roots
A quadratic equation with rational roots is a polynomial equation of degree 2 in which the coefficients and solutions are all rational numbers. This means that the equation can be written in the form ax^2 + bx + c = 0, where a, b, and c are rational numbers.
A quadratic equation has rational roots if the discriminant, b^2-4ac, is a perfect square. This means that the square root of the discriminant is a rational number.
The formula for finding the roots of a quadratic equation with rational roots is x = (-b ± √(b^2-4ac)) / 2a. This is known as the quadratic formula.
Yes, a quadratic equation can have rational roots even if the coefficients are not rational numbers. This can occur if the irrational coefficients cancel out when using the quadratic formula.
Quadratic equations with rational roots can be used to model various real-life situations such as projectile motion, profit and loss in business, and the shape of a parabolic antenna. They are also commonly used in engineering and physics to solve problems involving motion and forces.