Polynomials: Quadratic Equation and Highest Degree Term
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Class X: Maths Chapter 2: Polynomials Top Concepts: 1. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. 2. 3. 4. A polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax + b, zero of the polynomial will be given by the expression (-b/a). 5. The number of real zeros of the polynomial is the number of times its graph touches or intersects x axis. 6. 7. 8. 9. 10. A polynomial p(x) of degree n will have atmost n real zeroes A linear polynomial has atmost one real zero. A quadratic polynomial has atmost two real zeroes. A cubic polynomial has atmost three real zeroes. Division algorithm can also be used to find the zeroes of a polynomial. If ‘a’ and ‘b’ are two zeroes of a fourth degree polynomial f(x), then other two zeroes can be found out by dividing f(x) by (x-a)(x-b) 11. If f(x) = q(x) g(x) + r(x), and r(x) = 0 then polynomial g(x) is a factor of polynomial f(x). 12. Process of dividing a polynomial f(x) by another polynomial g(x) is as follows: Step1: To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process. Step2: To obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor. Then again carry out the division process Step3: Continue the process till the degree of the new dividend is less that the degree of the divisor. This will be called the remainder.
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Class X: Maths Chapter 2: Polynomials Top Concepts: 1. The graph of a polynomial p(x) of degree n can intersects or touch the x axis at atmost n points. 2. 3. 4. A polynomial of degree n has at most n distinct real zeroes. The zero of the polynomial p(x) satisfies the equation p(x) = 0. For any linear polynomial ax + b, zero of the polynomial will be given by the expression (-b/a). 5. The number of real zeros of the polynomial is the number of times its graph touches or intersects x axis. 6. 7. 8. 9. 10. A polynomial p(x) of degree n will have atmost n real zeroes A linear polynomial has atmost one real zero. A quadratic polynomial has atmost two real zeroes. A cubic polynomial has atmost three real zeroes. Division algorithm can also be used to find the zeroes of a polynomial. If ‘a’ and ‘b’ are two zeroes of a fourth degree polynomial f(x), then other two zeroes can be found out by dividing f(x) by (x-a)(x-b) 11. If f(x) = q(x) g(x) + r(x), and r(x) = 0 then polynomial g(x) is a factor of polynomial f(x). 12. Process of dividing a polynomial f(x) by another polynomial g(x) is as follows: Step1: To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process. Step2: To obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor. Then again carry out the division process Step3: Continue the process till the degree of the new dividend is less that the degree of the divisor. This will be called the remainder.
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