This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5

This is an important ques and asked in paper

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

Question no. 4 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Let us consider the number be ‘x’

So according to the question,

5x = 2x

^{2}– 32x

^{2}– 3 – 5x = 02x

^{2}– 5x – 3 = 0Let us factorize,

2x

^{2}– 6x + x – 3 = 02x(x – 3) + 1(x – 3) = 0

(x – 3) (2x + 1) = 0

So,

(x – 3) = 0 or (2x + 1) = 0

x = 3 or 2x = -1

x = 3 or x = -1/2

∴ The required number is 3 [since, -1/2 cannot be a whole number].