Question 22382: Explain what the Zero-Product Principle is and give an example of how it is used to solve a quadratic equation in standard form
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! IN PROBLEMS OF NUMERICAL AND ALGEBRAIC QUANTITIES ,WE OFTEN COME ACROSS A PRODUCT OF NUMBER OF FACTORS BEING EQUAL TO ZERO .IN SUCH A CASE ATLEAST ONE OR MORE FACTORS WILL HAVE TO BE EQUAL TO ZERO ,SO AS TO MAKE THE PRODUCT ZERO.
FOR EX. IF X * Y * Z *T *....ETC..IS ZERO, THEN ONE OF THEM AT LEAST WILL BE ZERO.THAT IS X=0 OR Y=0 OR Z =0...ETC..
NOW WHEN WE FACTORISE THE GIVEN ALGEBRAIC EXPRESSION,A POLYNOMIAL OF HIGHER DEGREE SAY , WE FINALLY END UP WITH A NUMBER OF SMALLER DEGREE POLYNOMIALS AS FACTORS WHOSE PRODUCT WILL EQUAL THE GIVEN HIGHER DEGREE POLYNOMIAL.HENCE BY THE ABOVE PRINCIPAL ,IF THE GIVEN HIGHER DEGREE POLYNOMIAL IS EQUAL TO ZERO THEN , ONE OF THE SMALLER DEGREE POLYNOMIAL FACTORS SHALL BE EQUAL TO ZERO .THIS ENABLES US TO SOLVE THE EQUATION BY WORKING ON THE LOWER DEGREE POLYNOMIALS AS AGAINST THE ORIGINAL HIGHER DEGREE POLYNOMIALS.
IF THE GIVEN ORIGINAL EQUATION IS A QUADRATIC OR SECOND DEGREE POLYNOMIAL , WE GET 2 FIRST DEGREE FACTORS WHICH COULD BE EASILY SOLVED TO GET THE VALUE OF UNKNOWN.FOR EXAMPLE
IF A GIVEN QUADRATIC IN STANDARD FORM IS
X^2-5X+6=0
IT CAN BE FACTORISED TO GET (X-3)(X-2)=0
HENCE BY THE ABOVE PRINCIPLE X-3 =0 OR X-2 =0 ...HENCE
X=3 OR X=2...WHICH IS A WAY OF SOLVING QUADRATIC EQUATIONS.
|
|
|
