3x2 + 12x = - 1
ie 3x2 + 12x + 1 = 0 has no rational roots.
The irrational roots are [-12 +/- sqrt(132)]/6 = -3.915 and -0.085
1 and 3
8x-3+6x-1 = 12x+614x-4 = 12x+614x-12x = 6+42x = 10x = 5
3x+12x = 15 15x = 15 x = 1
2+2=4-1=3x2=6
No. Y=3X2+1 is a Binomial Equation.
1 and 3
The equation is equivalent to: -3x2 - 12x - 1 = 0 [you could change signs to get 3x2 + 12x + 1 = 0 but that is not required] The discriminant is (-12)2 - 4*(-3)(-1) = 144 - 12 = 132
6y
8x-3+6x-1 = 12x+614x-4 = 12x+614x-12x = 6+42x = 10x = 5
3x+12x = 15 15x = 15 x = 1
x2+12x+11=0 (x+11)(x+1)=0 x=-11 or x=-1
3x2 + 22x + 7 = 3x2 +21x + x + 7 = 3x(x + 7) + (x + 7) = (x + 7)(3x + 1)
2+2=4-1=3x2=6
No. Y=3X2+1 is a Binomial Equation.
No solution. Multiply second equation by 3 and get 12x + 6y = 0 but already stated 12x + 6y = 9...
3x2 + 27x = 30 ∴ x2 + 9x - 10 = 0 ∴ (x + 10)(x - 1) = 0 ∴ x ∈ {-10, 1}
x2+8x = -3x2+5 4x2+8x-5 = 0 (2x+5)(2x-1) = 0 x = -5/2 or x = 1/2