The discriminant is 33.
The discriminant of the equation ... (b2-4ac) = (225-160) ... is real and positive, so the roots are real and unequal.
Discriminant = b2-4ac = (-2)2-(4*4*4) = -60
The discriminant is 0.
72-4*4*4 = -15 The discriminant is less than zero so there's no solutions to the quadratic equation.
The coefficients are a = 4, b = -3, c = -8. The discriminant is calculated with the formula b2 - 4ac, so just replace the coefficients in this formula.
zero
It has 2 real solutions because the discriminant is greater than zero.
4x2 plus 3=11
It can't be factored because the discriminant is less than zero.
2.
x2-5-4x2+3x = 0 -3x2+3x-5 = 0 or as 3x2-3x+5 = 0
If the discriminant b2-4ac of the quadratic equation equals zero then it will have two equal roots meaning that the line is tagent to the curve. So by implication: (2x+1.25)(2x+1.25) = 10x 4x2-5x+25/16 = 0 Hence use the discriminant of b2-4ac :- (-5)2-4*4*25/16 = 0 Therefore the discriminant equals 0 so the line will be tangent to the curve. In fact working out the equation gives x having two equal roots of 5/8