3x-4-4x-3-7x-2-4x-5-0-x-

Question Number 58046 by ANTARES VY last updated on 17/Apr/19

3 x^{4} - 4 x^{3} - 7 x^{2} - 4 x + 5 = 0

x = ?

Answered by tanmay last updated on 17/Apr/19

f (x) = 3 x^{4} - 4 x^{3} - 7 x^{2} - 4 x + 5

f (0) = 5 s o f (0) > 0

f (1) = - 7 f (1) < 0

s i n c e f (0) > 0 a n d f (1) < 0

s o o n e r o o t l i e s b e t w e e n (0, 1) \leftarrow l o o k h e r e

f (2) = 48 - 32 - 28 - 8 + 5

= 53 - 68 = - 15

s i n c e f (1) < 0 a n d f (2) < 0

s o n o r o o t b e t w e e n (1, 2) \leftarrow l o o k h e r e

f (3) = 243 - 108 - 28 - 8 + 5

= 248 - 144

= 104

f (3) > 0

s i n c e f (2) < 0 a n d f (3) > 0

s o o n e r o o t b e t w e e n (2, 3) \leftarrow l o o k h e r e

f (4) = 389 f (4) > 0

s i n c e f (3) > 0 a n d f (4) > 0

s o n o r o o t b e t w e e n (3, 4)

i h a v e t r i e d t o f i n d t h e l o c a t i o n o f r o o t s . .

Answered by MJS last updated on 17/Apr/19

x_{1} \approx . 571581

x_{2} \approx 2.41140

x_{3} \approx - . 824822 - . 727241

x_{4} \approx - . 824822 + . 727241

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