In the Maths test two representatives, while solving a quadratic … - Vidyadip

MCQ

In the Maths test two representatives, 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.

A
$x^2+4 x+14=0$
B
$2 x^2+7 x-24=0$
✓
$x^2-14 x+48=0$
D
$3 x^2-17 x+52=0$

✓

Answer

Correct option: C.

$x^2-14 x+48=0$

(c) : Since, $1^{\text {st }}$ person made a mistake in constant term. Therefore, sum of roots $=14$ and $2^{\text {nd }}$ person made a mistake in coefficient of $x$
$\therefore \quad$ Product of roots $=48$
$\Rightarrow$ Required quadratic equation is
$x^2-14 x+48=0$

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