The browser that is used for submitting questions does not permit many mathematical symbols. It is therefore not possible to be sure what the question was. For a quadratic equation of the form y = ax^2 + bx + c, where a, b and c are real numbers and a is non-zero, the discriminant is b^2 – 4ac.
6^2 -4(3*30) = -96 meaning that the given quadratic expression has no real roots
x3 + 3x2 - 6x - 8 = (x - 2)(x2 + 5x + 4) = (x - 2)(x + 1)(x + 4)
The discriminant is -32.
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x + 2) - 4(x + 2) = (x + 2)(3x - 4).
(3x2 - 6x)/3x = 3x(x-2)/3x = x-2, for x<>0
The operator (+ or -) before the 5 (and before the 6, but that doesn't matter for the discriminant) is missing from the question, so:If it is 3x2 ± 6x + 5, thendiscriminant = (±6)2 - 4 x 3 x 5 = 36 - 60 = -24 If it is 3x2 ± 6x - 5, thendiscriminant = (±6)2 - 4 x 3 x (-5) = 36 + 60 = 96
b^2 - 4ac Is the discriminant. 6^2 - 4(3)(5) 36 - 60 = - 24 < 0 so, an unreal answer and no real X intercepts
6^2 -4(3*30) = -96 meaning that the given quadratic expression has no real roots
3X2 + 6X + 9 3(X2 + 2 + 3) -----------------------3 is a common factor of all terms
-3x2 = 5 + 3x (add 3x2 to both sides)0 = 3x2 + 5 + 3x or3x2 + 3x + 5 = 0 (since the discriminant is less than zero, we have complex roots)x = [-3 ± √[(32 - 4(3)(5)]]/2(3)x = [-3 ± √(9 - 60)]/6x = (-3 ± √-51)/6x = (-3 ± i√51)/6x = (-3 + i√51)/6 = -1/2 + (√51/6)i orx = (-3 - i√51)/6 = -1/2 - (√51/6)i
x3 + 3x2 - 6x - 8 = (x - 2)(x2 + 5x + 4) = (x - 2)(x + 1)(x + 4)
In this case, the discriminant is less than zero and the graph of this parabola lies above the x-axis. It never crosses.
-6x + 9x2 - 24 = 3(3x2 - 2x - 8) = 3(3x2 - 6x + 4x - 8) = 3(3x(x - 2) + 4(x - 2)) = 3(3x + 4)(x - 2)
The discriminant is -32.
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x + 2) - 4(x + 2) = (x + 2)(3x - 4).
6x(3x2 - x + 4)
3x2 - 7x + 2 = 3x2 - 6x - x + 2 = 3x(x - 2) - 1(x - 2) = (3x - 1)(x - 2) So x = 1/3 or x = 2