In the Maths test two students, 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 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 correct quadratic equation.

x^{2} - 44 x + 14 = 0

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2 x^{2} + 7 x - 24 = 0

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x^{2} - 14 x + 48 = 0

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3 x^{2} - 17 x + 52 = 0

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Solution

The correct option is C $x^{2} - 14 x + 48 = 0$
Since the first person made a mistake in constant term.
Therefore, the sum of roots = 14
and the second person made a mistake in coefficient of x
Therefore, product of roots = 48
Required quadratic equation is $x^{2} - 14 x + 48 = 0$

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In a Math test two students while solving a quadratic equation committed the following mistakes:
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(ii) Another one committed an error in the coefficient of x and 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 correct quadratic equation.

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The correct option is C x2−14x+48=0 Since the first person made a mistake in constant term. Therefore, the sum of roots = 14 and the second person made a mistake in coefficient of x Therefore, product of roots = 48 Required quadratic equation is x2−14x+48=0

The correct option is C $x^{2} - 14 x + 48 = 0$
Since the first person made a mistake in constant term.
Therefore, the sum of roots = 14
and the second person made a mistake in coefficient of x
Therefore, product of roots = 48
Required quadratic equation is $x^{2} - 14 x + 48 = 0$