Q. 224.3( 3 Votes )

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Answer :

To find: Marks in two subjects


Method Used:


To solve the quadratic equation by factorisation method, follow the steps:


1) Multiply the coefficient of x2 and constant term.


2) factorise the result obtained in step 1.


3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them


You get coefficient of x.


Explanation:


Let the marks obtained in Mathematics by P be ‘a’.


Given, sum of the marks obtained by P in Mathematics and science is 28.


Marks obtained in science = 28 – a


Also, if he got 3 marks more in Mathematics and 4 marks less in Science, product of his marks, would have been 180.


(a + 3) (28 – a – 4) = 180


-a2 + 21a + 72 = 180


a2 – 21a + 108 = 0


a2 – 12a – 9a + 108 = 0


a (a – 12) – 9(a – 12) = 0


(a – 9) (a – 12) = 0


a = 9 or 12


If marks obtained is Mathematics is 9,


Marks in science = 28 – a


= 28 – 9


= 19


And


If marks obtained is Mathematics is 12,


Marks in science = 28 – a


= 28 – 12


= 16


Thus, marks obtained in science = 19 or 16


Marks in Mathematics = 12, Marks in Science = 16


Or


Marks in Mathematics = 9, Marks in Science = 19


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