Which of the following quadratic equations is not solvable by grouping?(1 point) Responses 2x2−2x−10=0 2 x squared minus 2 x minus 10 equals 0 x2−12x+35=0 x squared minus 12 x plus 35 equals 0 x2−2x+1=0 x squared minus 2 x plus 1 equals 0 2x2+14x+12=0
The quadratic equation that is not solvable by grouping is 2x^2+14x+12=0.
To determine which quadratic equation is not solvable by grouping, we need to consider the quadratic equation's discriminant. The discriminant is the expression inside the square root in the quadratic formula. If the discriminant is negative, the quadratic equation does not have real solutions and is not solvable.
The quadratic formula is given by:
x = (-b ± √(b^2-4ac)) / (2a)
Let's calculate the discriminant for each of the given equations:
1) 2x^2 - 2x - 10 = 0
a = 2, b = -2, c = -10
Discriminant: b^2 - 4ac = (-2)^2 - 4(2)(-10) = 4 + 80 = 84
Since the discriminant (84) is positive, this equation is solvable by grouping.
2) x^2 - 12x + 35 = 0
a = 1, b = -12, c = 35
Discriminant: b^2 - 4ac = (-12)^2 - 4(1)(35) = 144 - 140 = 4
Since the discriminant (4) is positive, this equation is solvable by grouping.
3) x^2 - 2x + 1 = 0
a = 1, b = -2, c = 1
Discriminant: b^2 - 4ac = (-2)^2 - 4(1)(1) = 4 - 4 = 0
Since the discriminant (0) is equal to zero, this equation is solvable by grouping.
4) 2x^2 + 14x + 12 = 0
a = 2, b = 14, c = 12
Discriminant: b^2 - 4ac = (14)^2 - 4(2)(12) = 196 - 96 = 100
Since the discriminant (100) is positive, this equation is solvable by grouping.
Therefore, all of the given quadratic equations have a positive or zero discriminant. Hence, all the quadratic equations mentioned in the options are solvable by grouping.