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 x^{2} 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

⇒ -a^{2} + 21a + 72 = 180

⇒ a^{2} – 21a + 108 = 0

⇒ a^{2} – 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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