In the Maths Olympiad of 2020 at Animal Planet, two representatives fr

1.	In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes.(i) One of them made a mistake in the constant term and got the roots as 5 and 9.(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.(A) x2 + 4x + 14 = 0(B) 2x2 + 7x - 24 = 0(C) x2 - 14x + 48 = 0(D) 3x2 - 17x + 52 = 0
Answer» The correct option is: (C) x² - 14x + 48 = 0 Explanation: For 1^st one, Let the equation be x² + ax + b = 0 Since roots are 5 and 9 .'. a = -14 and b = 45 For 2^ndone, Let the equation be x² + px + q - 0 Since roots are 12 and 4. . ^.. p = -16 and q = 48 Now, according to the question, b and p both are wrong. Therefore, the correct equation would be x² -14x + 48 = 0

In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes.(i) One of them made a mistake in the constant term and got the roots as 5 and 9.(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.(A) x2 + 4x + 14 = 0(B) 2x2 + 7x - 24 = 0(C) x2 - 14x + 48 = 0(D) 3x2 - 17x + 52 = 0

Answer»

The correct option is: (C) x² - 14x + 48 = 0

Explanation:

For 1^st one,

Let the equation be x² + ax + b = 0

Since roots are 5 and 9

.'. a = -14 and b = 45

For 2^ndone,

Let the equation be x² + px + q - 0

Since roots are 12 and 4.

. ^.. p = -16 and q = 48

Now, according to the question, b and p both are wrong.

Therefore, the correct equation would be

x² -14x + 48 = 0