Main Concepts and Results • Quadratic equation : A quadratic equation in скачать в хорошем качестве

Main Concepts and Results • Quadratic equation : A quadratic equation in

#class10 #quadraticequations Main Concepts and Results • Quadratic equation : A quadratic equation in the variable x is of the form ax2 + 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 ax2 + bx + c = 0, if aα2 + bα + c = 0. • The roots of the quadratic equation ax2 + bx + c = 0 are the same as the zeroes of the quadratic polynomial ax2 + 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 ax2 + bx + c = 0 can be found by equating to zero the linear factors of ax2 + 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 x2 and x terms in the quadratic equation so that they become a complete square, and solve for x. • Quadratic Formula : If b2 – 4ac ≥ 0, then the real roots of the quadratic equation ax2 + bx + c = 0 are given by 2 4 2 2 − − ± b b ac a a . • The expression b2 – 4ac is called the discriminant of the quadratic equation. • Existence of roots of a quadratic equation: A quadratic equation ax2 +bx+c=0 has