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Question
Shriya and Vidya solved a quadratic equation. While solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. Which of the following are correct about the correct roots of the equation?
Shriya and Vidya solved a quadratic equation. While solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. Which of the following are correct about the correct roots of the equation?
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Solution
The correct options are
A One of the correct roots is -1.
D One of the correct roots is 3.
Shriya made a mistake in constant term only,
Thus, the sum of the roots was correct.
Sum of roots=2=−ba
Vidya made a mistake only in coefficient of x
So the product of roots was correct.
Thus,
Product of roots=−3=ca
Hence, the correct quadratic equation is x2–2x−3=0
Solving the above quadratic equation we get x=−1,3.
A
One of the correct roots is -1.
D
One of the correct roots is 3.
Shriya made a mistake in constant term only,
Thus, the sum of the roots was correct.
Sum of roots=2=−ba
Vidya made a mistake only in coefficient of x
So the product of roots was correct.
Thus,
Product of roots=−3=ca
Hence, the correct quadratic equation is x2–2x−3=0
Solving the above quadratic equation we get x=−1,3.
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