what two numbers adds to -5 but multiplies to -14
Mathematics · High School · Tue Nov 03 2020
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Let the numbers be a and b
a+b = -5 …..(1)
and a*b = -14 …..(2)
From equation (1)
a= -5 -b …..(3)
now putting value of a in equation (2)
(-5-b)*b = -14
-5b - b^2 = -14
b^2 + 5b -14 = 0
b^2 + 7b - 2b -14=0
b(b +7) - 2 (b +7) =0
(b+7) (b-2) =0
now, b+7 =0
b = -7
and, b-2 =0
b= 2
Now, substituting value of b in equation (3)
we get, a = -5 +7
a = 2
and , a =-5 -2
a = -7
a = -7
Thus, either of a and b could be 2 and -7 to give -5 when adding and -14 when multiplying.