Question

find two numbers whose sum is 12 and whose product is is -160

Answer 1

Answer:

first number is 20 .... and second is -8

Answer 2

$Given \: sum \: of \: two \: numbers = 12$

$Let \: One \: number = x$

$Second \: number = ( 12 - x )$

$\blue { Product \: of \: two \: numbers = -160}$

$\implies x( 12 - x ) = -160$

$\implies 12x - x^{2} + 160 = 0$

/* Multiplying bothsides by (-1) , we get */

$\implies -12x + x^{2} - 160 = 0$

$\implies x^{2} - 12x - 160 = 0$

/* Splitting the middle term,we get */

$\implies x^{2} + 8x - 20x - 160 = 0$

$\implies x( x + 8 ) - 20( x + 8 ) = 0$

$\implies ( x + 8 )( x - 20 ) = 0$

$\implies x + 8 = 0 \: Or \: x - 20 = 0$

$\implies x = -8 \: Or \: x = 20$

$i ) If \: x = -8 \: then \\One \: number = -8$

$Second \: number = 12 - x \\= 12 - (-8) \\= 12 + 8 \\= 20$

$ii ) If \: x = 20 \: then \\One \: number = 20$

$Second \: number = 12 - 20 \\= -8$

Therefore.,

$\red{ Required \: two \: numbers \: are } \\\green { -8 \: and \: 12 }$

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