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प्रश्न
Construct a word problem on quadratic equation, such that one of its answers is 20 (years, rupees, centimeter, etc.). Also, solve it.
उत्तर
Find the roots of a equation x² - 10x = 200
x² - 10x = 200
=> x² - 10x - 200 = 0
=> x² - 20x + 10x - 200 = 0
=> x(x - 20) + 10(x - 20) = 0
=> (x + 10)(x-20) = 0
=> x = 20 or x = -10
hence one of its answer is 20
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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
