Advertisements
Advertisements
Question
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
Advertisements
Solution
Let number = x
Now according to the condition,
5x = 2x2 - 3
⇒ 2x2 - 5x - 3 = 0
⇒ 2x2 - 6x + x - 3 = 0
⇒ 2x(x - 3) + 1 (x - 3) = 0
⇒ (x - 3)(2x + 1) = 0
Either x - 3 = 0,
then x = 3
or
2x + 1 = 0,
then 2x = -1
⇒ x `-(1)/(2)`
But it is not possible as the number is whole number.
∴ Number = 3.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
Find three successive even natural numbers, the sum of whose squares is 308.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children.
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
Using quadratic formula find the value of x.
p2x2 + (p2 – q2)x – q2 = 0
