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Questions
Which one is the quadratic equation?
From the following equations which one is the quadratic equation?
Options
`5/x - 3 = x^2`
x(x + 5) = 2
n – 1 = 2n
`1/x^2(x + 2) = x`
Solution
x(x + 5) = 2
Explanation:
The general form of a quadratic equation is ax2 + bx + c = 0.
i. `5/x - 3 = x^2`
`(5 - 3x)/x = x^2`
5 – 3x = x3
x3 + 3x – 5 = 0
⇒ This is not a quadratic equation.
ii. x(x + 5) = 2
x2 + 5x = 2
x2 + 5x − 2 = 0
⇒ This is a quadratic equation.
iii. n − 1 = 2n
This is not a quadratic equation.
iv. `1/x^2 (x + 2) = x`
x + 2 = x3
x3 – (x + 2) = 0
x3 – x – 2 = 0
⇒ This is not a quadratic equation.
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Solution:
We need one of the solutions of the quadratic equation as 5.
Then we can take another root as any number like a positive or negative number or zero. Here I am taking another root of the quadratic equation as 2.
Then we can form a word problem as below,
Smita is younger than her sister Mita by 3 years (5 – 2 = 3). If the product of their ages is (5 × 2 = 10). Then find their present ages.
Let the age of Mita be x.
Therefore age of Smita = x – 3
By the given condition,
x(x – 3) = 10
x2 – 3x – 10 = 0
