Question

If the sum of two integers is $-2$ and their product is $-24$, the numbers are

• A. $6$ and $4$
• B. $-6$ and $4$
• C. $-6$ and $-4$
• D. $6$ and $-4$

Answer 1

Answer: (B)

$-6$ and $4$

Let $p$ and $q$ be the required integers

If $p+q$ and $pq$ are known then quadratic equation corresponding to roots as $p$ and $q$ is given by,

$x^2-(p+q)x+pq=0$

$\Rightarrow x^2+2x-24=0$, substitute the given values

$\Rightarrow x^2+6x-4x-24=0$, split the middle term

$\Rightarrow (x^2+6x)+(-4x-24)=0$, group pair of terms

$\Rightarrow x(x+6)-4(x+6)=0$, factor each binomials

$\Rightarrow (x+6)(x-4)=0$, factor out common factor

$\Rightarrow x=-6$ or $x=4$, set each factor to $0$

Hence $p$ and $q$ are $-6$ and $4$