In the Maths test two students, committed the following mistakes while solving a quadratic equation :
(i) One of them made a mistake in the constant term and got the roots as 2 and 4.
(ii) Another one committed an error in the coefficient of x and got the roots as 3 and 5.
But, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

$x^{2} + 6 x + 15 = 0$

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$x^{2} + 15 x - 6 = 0$

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$x^{2} - 6 x + 15 = 0$

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$x^{2} - 17 x + 6 = 0$

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Solution

The correct option is C
$x^{2} - 6 x + 15 = 0$

Since the first person made a mistake in constant term.
Therefore, the sum of roots = 2 + 4 = 6
and the second person made a mistake in coefficient of x
Therefore, product of roots = 3 $\times$ 5 = 15
Required quadratic equation is $x^{2} - 6 x + 15 = 0$

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The correct option is C x2−6x+15=0 Since the first person made a mistake in constant term. Therefore, the sum of roots = 2 + 4 = 6 and the second person made a mistake in coefficient of x Therefore, product of roots = 3 × 5 = 15 Required quadratic equation is x2−6x+15=0