Flashcards
Set
Cards in this deck (9)
- 1SetSet is a collection of well defined objects which are distinct from each other. Sets are usually denoted by capital letters A, B,C,… and elements are usually denoted by small letters a, b,c,…
- 2Real Polynomial:Let a0, a1, a2, … , an be real numbers and x is a real variable. Then, f(x) = a0 + a1x + a2x2 + … + anxn is called a real polynomial of real variable x with real coefficients.
- 3Complex Polynomial:If a0, a1, a2, … , an be complex numbers and x is a varying complex number, then f(x) = a0 + a1x + a2x2 + … + an – 1xn – 1 + anxn is called a complex polynomial or a polynomial of complex variable with complex coefficients.
- 4Degree of a Polynomial:A polynomial f(x) = a0 + a1x + a2x2 + a3x3 + … + anxn , real or complex is a polynomial of degree n , if an ≠ 0.
- 5Polynomial Equation:If f(x) is a polynomial, real or complex, then f(x) = 0 is called a polynomial equation. If f(x) is a polynomial of second degree, then f(x) = 0 is called a quadratic equation .
- 6Quadratic Equation:A polynomial of second degree is called a quadratic polynomial. Polynomials of degree three and four are known as cubic and biquadratic polynomials respectively. A quadratic polynomial f(x) when equated to zero is called quadratic equation. i.e., ax2 + bx + c = 0 where a ≠ 0.
- 7Roots of a Quadratic Equation:The values of variable x .which satisfy the quadratic equation is called roots of quadratic equation.
- 8Important Points to be RememberedAn equation of degree n has n roots, real or imaginary .
- 9—Surd and imaginary roots always occur in pairs of a polynomial equation with real coefficients i.e., if (√2 + √3i) is a root of an equation, then’ (√2 – √3i) is also its root. .