# In a class test,

Let the marks obtained by P in mathematics and science be x and (28 – x) respectively

According to the given condition,

(x + 3)(28 – x – 4) = 180

(x + 3)(24 – x) = 180

– x2 + 21x + 72 = 180

x2 – 21x + 108 = 0

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = – 21 c = 108

= 1.108 = 108

And either of their sum or difference = b

= – 21

Thus the two terms are – 12 and – 9

Difference = – 12 – 9 = – 21

Product = – 12. – 9 = 108

x2 – 12x – 9x + 108 = 0

x (x – 12) – 9 (x – 12) = 0

(x – 12) (x – 9) = 0

(x – 12) = 0 or (x – 9) = 0

x = 12, x = 9

When x = 12,

28 – x = 28 – 12 = 16

When x = 9,

28 – x = 28 – 9 = 19

Hence he obtained 12 marks in mathematics and 16 science or

He obtained 9 marks in mathematics and 19 science.

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