Question

Which of the following quadratic equations is not solvable by grouping?(1 point)
Responses

x2−2x+1=0
x squared minus 2 x plus 1 is equal to 0

2x2+14x+12=0
2 x squared plus 14 x plus 12 is equal to 0

2x2−2x−10=0
2 x squared minus 2 x minus 10 is equal to 0

x2−12x+35=0

Answer 1

2x^2 − 2x − 10 = 0

Reason: the others factor easily:
- x^2 − 2x + 1 = (x − 1)^2
- 2x^2 + 14x + 12 = 2(x + 1)(x + 6)
- x^2 − 12x + 35 = (x − 5)(x − 7)

For 2x^2 − 2x − 10, dividing by 2 gives x^2 − x − 5, and there are no integer (or rational) numbers whose product is −5 and sum is −1, so it cannot be split for grouping. (Its roots are (1 ± √21)/2 by the quadratic formula.)