[PDF] QUADRATIC EQUATIONS Quadratic equation : A quadratic equation

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(A) Main Concepts and Results •Quadratic equation : A quadratic equation in the variable x is of the form ax 2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0. •Roots of a quadratic equation : A real number α is said to be a root of the quadratic equation ax 2 + bx + c = 0, if aα 2 + bα + c = 0.•The roots of the quadratic equation ax 2 + bx + c = 0 are the same as the zeroes of the quadratic poblynomial ax 2 + bx + c. •Finding the roots of a quadratic equation by the method of factorisation : If we can factorise the quadratic polynomial ax2 + bx + c, then the roots of the quadratic equation ax 2 + bx + c = 0 can be found by equating to zero the linear factors of ax 2 + bx + c.•Finding the roots of a quadratic equation by the method of completing the square : By adding and subtracting a suitable constant, we club the x 2 and x terms

in the quadratic equation so that they become a complete square, and solve for x.•Quadratic Formula : If b

2 - 4ac ≥ 0, then the real roots of the quadratic equation ax 2 + bx + c = 0 are given by 2 4 22
b b ac aa •The expression b 2 - 4ac is called the discriminant of the quadratic equation. •Existence of roots of a quadratic equation: A quadratic equation ax2 +bx+c=0 has

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