Advertisements
Advertisements
Question
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
Advertisements
Solution
Let the required integer be x.
Then according to the given condition
⇒ x + x2 = 90
⇒ x2 + x - 90 = 0
⇒ x2 + 10x - 9x - 90 = 0
⇒ x(x + 10) - 9(x +10) = 0
⇒ (x +10) (x - 9) = 0
⇒ x + 10 = 0 or x - 9 = 0
⇒ x = -10 or x = 9
Hence, the required integer is 9 or -10.
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
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.
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
