Answer:
Two complex roots.
Step-by-step explanation:
F(x)=2x^4 +5x^3 - x^2 +6x-1
is a polynomial in x of degree 4.
Hence F(x) has 4 roots. There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.
Use remainder theorem to find the roots of the polynomial.
F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0
There is a change of sign in F from 0 to 1
Thus there is a real root between 0 and 1.
Similarly by trial and error let us find other real root.
F(-3) = -1 and F(-4) = 94
SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.
Other two roots are complex roots since no other place F changes its sign
In expanded form it is 4 + 0.7 + 0.02
Answer:
Right triangles:
5) 0.75, 1, 1.25
6) 18, 80,82
Not right triangles:
1) 5,5,√50
2) 6.5, 3.2, 7.8
3) √2, √3, 4
4) 12, 13, 20
Step-by-step explanation:
Right triangles: (for right triangles the Pythagorean theorem is true)
6) 18² + 80² = 82²
6724=6724
5) 0.75² + 1² = 1.25²
1.5625 =1.5625
Not right triangles:
1) 5² + 5² ≠(√50)²
1250≠ 50
2) 6.5² + 3.2² ≠ 7.8²
52.49≠60.84
3) (√2)² +(√3)² ≠ 4²
5≠ 16
4) 12² + 13² ≠ 20²
313 ≠ 400
