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Question
Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. (For the formation of word problems you can use quantities like age, rupees, or natural numbers.) (Sample solution for the above example is given below students can take another number to form another example)
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
Solution
Word problem:
The product of two consecutive natural numbers is 30. Find the numbers.
Answer:
Let the first natural number be x.
∴ The second consecutive natural number = x + 1
According to the given condition,
x(x + 1) = 30
∴ x2 + x = 30
∴ x2 + x – 30 = 0, which is the required quadratic equation.
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