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 = 2x2 – 3
2x2 – 3 – 5x = 0
2x2 – 5x – 3 = 0
Let us factorize,
2x2 – 6x + x – 3 = 0
2x(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].