how to know if the roots are real Some methods for finding the roots are Factorization method Quadratic Formula Completing the square method All the quadratic equations with real roots can be factorized The physical significance of the roots is that
To find the roots of an equation ax 2 bx c 0 by factoring factor its left side part set each of the factors to zero and solve The roots of a quadratic equation ax 2 bx c 0 are the values of the variable x that satisfy the equation Question 1 What are the nature of roots Answer The nature of roots simply means the category in which the roots are falling upon The roots may be imaginary real unequal or
how to know if the roots are real
how to know if the roots are real
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For roots to be real we need to calculate and show that ge 0 for all real values of h k and d Check that the equation is in standard form ax 2 bx c 0 Whether the discriminant is greater than zero equal to zero or less than zero can be used to determine if a quadratic equation has no real roots real and equal roots or real and unequal roots
From the conjugate root theorem we know that if the polynomial has real coefficients then if it has any nonreal root its roots will be a complex conjugate pair If it has real roots it could In your example computing f pm 2 3 and f 0 1 gives that f has one root each in 2 0 and 0 2 In the special case that f is a quadratic polynomial say f x ax 2
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To prove existence of roots of a continuous function you can exhibit changes of sign For instance f 10000 0 f 0 0 proves at least two roots Using pm infty like gimusi did is also possible Given a polynomial equation x n a n 1 x n 1 cdots a 1x a 0 0 where n is even and all the coefficients a i are real what is the best way to determine whether it has a real root
Find the real roots of each equation by factoring or using the Quadratic Formula Express the exact final simplified answers real numbers or simplified radical expressions x The Fundamental Theorem of Algebra can be used in order to determine how many real roots a given polynomial has Check it out
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how to know if the roots are real - For roots to be real we need to calculate and show that ge 0 for all real values of h k and d Check that the equation is in standard form ax 2 bx c 0