Question

Determine two integers whose sum is 6 and product is -6 ?
The first answer will be brainiest answer and will get followed by me.

Answer 1

Let the integers be x

so now x + x = 6

x=6-x

x ( 6-x)= -6

6x-x2=-6

x2-6x-6=0

x2-x+6x-6=0

x(x-1)+6(x-1)=0

(x-1)(x+6)=0

x-1=0 and x+6=0

x=1 and x=-6

Answer 2

let numbers be x and y

so, ATQ,

$x + y = 6.....(eq1) \\ x \times y = - 6.....(eq2) \\ susitute \: value \: of \: x \: from \: eq \: 1 \\ => x = 6 - y \\ x \times y = - 6 = (6 - y) \times y = - 6 \\ 6y - y {}^{2} = - 6$

-y² + 6y + 6 = 0

Comparing with Ax² + Bx + C = 0 (Shridharacharya method)

A = -1 ; B = 6 ; C = 6

$y( \alpha \beta ) = \frac{-(B)+- \sqrt{ {B}^{2} - 4AC} }{2A} \\ = \frac{-6 +- \sqrt{36 - 4 \times (-1) \times 6} }{2 \times (-1)} \\ = \frac{36 +- \sqrt{60} }{-2} \\ = \frac{36 +-2 \sqrt{15} }{-2} \\ = \frac{2(18 +- \sqrt{15} }{-2} \\ y( \alpha ) = - (18 + \sqrt{15} ) and y( \beta ) = - (18 - \sqrt{15} ) \\ y( \alpha ) = - (18 + 3.87) \: and \: y( \beta ) = - (18 - 3.87) \\ y( \alpha ) = - 21.87 \: and \: y( \beta ) = - 14.13</strong></p><p><strong>$

so 'y' is either -21.87 or -14.13

so x is either 27.87 or 20.13

Verification ----

x + y = 6

27.87 + (-21.87) = 27.87 -21.87 = 6 ; Hence Verified

Hope it helps

Mark Brainliest if it is correct !