given 685x^2 - 58x-976=0, if "m" and "n" two solutions of the equation, Then what is the value of 137m+137n

12.33

Step-by-step explanation:

To obtain the value of 137m + 137n, let us calculate the value of m and n.

NOTE: m and n are the solutions to the equation: 685x² – 58x – 976 = 0

Thus, we can obtain the solutions to equation by doing the following:

685x² – 58x – 976 = 0

a = 685

b = – 58

c = – 976

Using formula method:

x = – b ± √(b² – 4ac) ÷ 2a

x = – (–58) ± √(–58² – 4×685×–976) ÷ 2 × 685

= 58 ± √(3364 – – 2674240) ÷ 1370

= 58 ± √(3364 + 2674240) ÷ 1370

= 58 ± √(2677604) ÷ 1370

= 58 ± 1636.3386 / 1370

= (58 + 1636.3386) / 1370 or (58

– 1636.3386) / 1370

= 1694.3386 / 1370 or – 1578.3386/1370

x = 1.24 or –1.15

Thus,

m = 1.24

n = –1.15

Finally, we can obtain the value of

137m + 137n as shown below:

137m + 137n

m = 1.24

n = –1.15

= (137 × 1.24) + (137 × – 1.15)

= 169.88 + (– 157.55)

= 169.88 – 157.55

= 12.33

Thus, the value of 137m + 137n is 12.33