# Quadratic Equations Class 10 Notes Maths: Chapter 4

## Quadratic Equationsthe

- polynomial of degree 2 is called a quadratic polynomial. Its general form is ax
^{2}+ bx + c, where a, b and c are real numbers such that a ≠ 0 and x is a variable quantity. - If p(x) = ax
^{2}+ bx + c, a ≠ 0 is a quadratic polynomial and α is a real number, then p(α) = aα^{2}+ bα + c is known as the value of p(x) at x=α. - real number α is said to be a zero or root of the quadratic polynomial p(x) = ax
^{2}+ bx + c,if p(α) = 0 i.e., aα^{2}+ bα + c = 0 where a ≠ 0 and a, b and c are real numbers. - If p(x)=ax
^{2}+ bx + c is a quadratic polynomial, then p(x)=0, i.e., ax2 + bx + c = 0, a ≠ 0 is called a quadratic equation - The nature of the roots of the quadratic equation ax
^{2}+ bx + c = 0 depends upon the value of D = b^{2}– 4ac, where D is the discriminant of the quadratic equation - If ax
^{2}+ bx + c, a ≠ 0 is factorizable into a product of two linear factors, then the roots ofthe quadratic equation ax^{2}+ bx + c = 0 can be found by equating each factor to zero. - The roots of a quadratic equation ax
^{2}+ bx + c = 0, where a ≠ 0, can be found by using the formula

x = -b±(√ b2-4ac)/2a provided that b2 – 4ac ≥ 0. - The quadratic equation ax
^{2}+ bx + c = 0, a ≠ 0 has :

(i) two distinct real roots, if D = b^{2}– 4ac > 0

(ii) two equal real roots, if D = b^{2}– 4ac = 0

(iii) imaginary or no real roots, if D = b^{2}– 4ac < 08