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Find two numbers whose product is $-24$ and sum is 2.
Given:
Product of two numbers is $-24$ and their sum is 2.
To do:
We have to find the numbers.
Solution:
Let one of the numbers be x.
Thus implies,
The other number $=2-x$.
Therefore,
$x \times (2-x)=-24$
$2x-x^2=-24$
$x^2-2x-24=0$
Solving for $x$ by factorisation method, we get,
$x^2-6x+4x-24=0$
$x(x-6)+4(x-6)=0$
$(x-6)(x+4)=0$
$x-6=0$ or $x+4=0$
$x=6$ or $x=-4$
The two numbers are $-4$ and $6$.
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