math discriminant roots

Nature of the roots - Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square...

Without solving the quadratic equation, the nature of the roots can be determined using the discriminant. i) D >0 i.e., positive and not a perfect square. The roots are real and distinct (irrational). ii) D >0 i.e., perfect square. The roots are..

Which of the following can be the discriminant of the graph of the quadratic equation? => b 2 - 4 ac = 4 or b 2 - 4 ac = 0 or b 2 - 4 ac = 2 or b 2 - 4 ac = 8..

Find the square root of 144. => 14 or 22 or 24 or 12..

Find the square root of 324. => 16 or 17 or 14 or 18..

Find the cube root of 125. => 25 or 50 or 5 or 10..

Our investigation reveals that there is a definite relationship between the roots of a quadratic equation and the coefficient of the second term and the constant term. The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second..

To find the q th roots of a Complex number - One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2..

Summary - i) An expression of the form a 0 x n + a 1 x n - 1 +....+ a n = 0, where n is a positive integer and a 0 , a 1 ,...,a n belong to some number system F, is called a polynomial in the variable x over F. ii) The degree of polynomial is defined as the highest index of the variable x occurring..

Since square root of a negative number is not real, we define a function f : R + R such that ..