Nature Of Roots Of Quadratic Equation

Nature Of Roots Of Quadratic Equation. Nature of Roots of a Quadratic Equation Definition Formula Examples Discriminant Consider a quadratic equation a x 2 + b x + c = 0 where a is the coefficient of x 2 b is the coefficient Nature of the Roots of a Quadratic Equation Examples Find the discriminant of the quadratic equation 2 x.

Nature of Roots of Quadratic Equation (a) Consider the quadratic equation a x 2 + b x + c = 0 where a b c ∈ R & a ≠ 0 then x = − b ± D 2 a where D = b 2 – 4 a c So a quadratic equation a x 2 + b x + c = 0 (i) has no real roots if D < 0 (ii) has two equal real roots if D = 0 (iii) has two distinct real roots if D > 0.

Nature of Roots of Quadratic Equation Mathemerize

Examine the nature of the roots of the following quadratic equation 2×2 3x 1 = 0 Solution The given quadratic equation is in the general form ax 2 + bx + c = 0 Then we have a = 2 b = 3 and c = 1 Find the value of the discriminant b 2 4ac b 2 4ac = (3) 2 4 (2) (1) b 2 4ac = 9 + 8.

Nature of Roots of Quadratic Equation: Different Cases for D

A quadratic equation in its standard form is represented as \(ax^2 + bx + c\) = \(0\) where \(a~b ~and~ c\) are real numbers such that \(a ≠ 0\) and \(x\) is a variable The number of roots of a polynomial equation is equal to its degree So a quadratic equation has two roots Some methods for finding the roots are Factorization method Quadratic Formula Completing the square method.