Question

find the two numbers whose sum is -3 and product is -42

Answer 1

let the two numbers be x and y
x + y = -3.......i

xy=-42
y=-42/x
putting this in i
x + (-42/x) =-3
$x {}^{2} + 3x - 42 = 0$

solving this you'll get answer
x=(-3+√177)/2
y= -42 / (-3+√177)/2

Answer 2

The numbers are $\frac{-3 + \sqrt{159}i}{2}$ and $\frac{-3 - \sqrt{159}i}{2}$

Step-by-step explanation:

Let the two number be x and y

Sum of the numbers is -3

So, x+y=-3 ---1

Product of two numbers = -42

xy=-42

Substitute the value of x from 1

(-3-y)y=42

-3y-y^2=42

y^2+3y+42=0

General equation : $ax^2+bx+c=0$

$y = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ y = \frac{-3 \pm \sqrt{3^2-4(1)(42)}}{2}\\y= \frac{-3 + \sqrt{3^2-4(1)(42)}}{2}, \frac{-3 - \sqrt{3^2-4(1)(42)}}{2}}\\y= \frac{-3 + \sqrt{159}i}{2}, \frac{-3 - \sqrt{159}i}{2}$

Hence the numbers are $\frac{-3 + \sqrt{159}i}{2}$ and $\frac{-3 - \sqrt{159}i}{2}$

#Learn more:

Find two numbers whose sum is 12 and whose product is 35​

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