Page 1 (Quadratic equation is an equation in which the highest power of an unknown variable is 2) 1. Quadratic Equation: Any equation of the form p(x) = 0, where p(x) is a polynomial of degree/power 2, is a quadratic equation. Example: , , , etc. 2. Standard Form of Quadratic Equation: When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation i.e. , where a, b, c are real numbers, a ? 0. 3. Methods to find roots/solutions of a quadratic equation: a. Factorization method b. Completing the square method c. Discriminant method Page 2 (Quadratic equation is an equation in which the highest power of an unknown variable is 2) 1. Quadratic Equation: Any equation of the form p(x) = 0, where p(x) is a polynomial of degree/power 2, is a quadratic equation. Example: , , , etc. 2. Standard Form of Quadratic Equation: When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation i.e. , where a, b, c are real numbers, a ? 0. 3. Methods to find roots/solutions of a quadratic equation: a. Factorization method b. Completing the square method c. Discriminant method 4. Solution of a Quadratic Equation by Factorization: a. A real number a is said to be a root of the quadratic equation , if we can say that x = a is a solution of the quadratic equation Note: b. If we factorize , a ? 0, into a product of two linear factors, then the roots of the quadratic equation can be found by equating each factor to zero. Example: The roots of are the values of x for which (3x – 2)(2x + 1) = 0 (3x – 2) = 0 or (2x + 1) = 0 Zeroes of the quadratic polynomial ?? ?? ???? ?? Roots of the quadratic equation ?? ?? ???? ?? Page 3 (Quadratic equation is an equation in which the highest power of an unknown variable is 2) 1. Quadratic Equation: Any equation of the form p(x) = 0, where p(x) is a polynomial of degree/power 2, is a quadratic equation. Example: , , , etc. 2. Standard Form of Quadratic Equation: When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation i.e. , where a, b, c are real numbers, a ? 0. 3. Methods to find roots/solutions of a quadratic equation: a. Factorization method b. Completing the square method c. Discriminant method 4. Solution of a Quadratic Equation by Factorization: a. A real number a is said to be a root of the quadratic equation , if we can say that x = a is a solution of the quadratic equation Note: b. If we factorize , a ? 0, into a product of two linear factors, then the roots of the quadratic equation can be found by equating each factor to zero. Example: The roots of are the values of x for which (3x – 2)(2x + 1) = 0 (3x – 2) = 0 or (2x + 1) = 0 Zeroes of the quadratic polynomial ?? ?? ???? ?? Roots of the quadratic equation ?? ?? ???? ?? Note: For equations with coefficient of ?? other than 1, divide the whole equation by the same number on both the sides to get 1 as the coefficient of ?? and then start the process of completing the square. 5. Solution of a Quadratic Equation by Completing The Square: Page 4 (Quadratic equation is an equation in which the highest power of an unknown variable is 2) 1. Quadratic Equation: Any equation of the form p(x) = 0, where p(x) is a polynomial of degree/power 2, is a quadratic equation. Example: , , , etc. 2. Standard Form of Quadratic Equation: When we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation i.e. , where a, b, c are real numbers, a ? 0. 3. Methods to find roots/solutions of a quadratic equation: a. Factorization method b. Completing the square method c. Discriminant method 4. Solution of a Quadratic Equation by Factorization: a. A real number a is said to be a root of the quadratic equation , if we can say that x = a is a solution of the quadratic equation Note: b. If we factorize , a ? 0, into a product of two linear factors, then the roots of the quadratic equation can be found by equating each factor to zero. Example: The roots of are the values of x for which (3x – 2)(2x + 1) = 0 (3x – 2) = 0 or (2x + 1) = 0 Zeroes of the quadratic polynomial ?? ?? ???? ?? Roots of the quadratic equation ?? ?? ???? ?? Note: For equations with coefficient of ?? other than 1, divide the whole equation by the same number on both the sides to get 1 as the coefficient of ?? and then start the process of completing the square. 5. Solution of a Quadratic Equation by Completing The Square: 6. Discriminant: A discriminant of a quadratic equation determines whether the quadratic equation has real roots or not. Note: Check point no. 7: Nature of the roots DISCRIMINANT = 7. Quadratic Formula: The roots of a quadratic equation are given by v Where, DISCRIMINANT (Discriminant = ) 8. Nature of the roots: A quadratic equation has a. Two distinct real roots, if b. Two equal roots, if c. No real roots, ifRead More

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