Divide 11 into two parts such that their product will be 24. | Quadratic Equation | SciPiPupil

Question: Divide 11 into two parts such that their product will be 24.

Solution:

According to the question,

Condition I,

11 is divided into two parts,

Let x be one part. Then, the other part is (11-x).

Condition II,

The product of above numbers is 24.

$or, x × (11-x) = 24$

$or, 11x - x^2 = 24$

$or, x^2 -11x +24 = 0$

$or, x^2 -(8+3)x +24 = 0$

$or, x^2 - 8x -3x +24 = 0$

$or, x(x -8) -3(x -8) = 0$

$or, (x -3)(x -8) = 0$

Either,

$x -3 = 0$

$\therefore x = 3$

Or,

$x -8 = 0$

$\therefore x = 8$

So, when x = 3, the other number is (11-3) = 8.

And, when x = 8, the other number is (11-8) = 3.

Therefore, the required two numbers are 3 and 8.

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