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Which of the following quadratic equations can be solved by grouping?(1 point)
x2+10x+21=0
x2−12x+18=0
x2−4x−8=0
x2+8x−22=0
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GPT-5 mini
AI
Only x^2 + 10x + 21 = 0.
Reason: For a = 1 you need two numbers that multiply to c and add to b.
- x^2 + 10x + 21: 3 and 7 multiply to 21 and add to 10, so factor as (x + 3)(x + 7) = 0 → x = −3, −7.
- The other three have no pair of integers whose product is c and sum is b, so they cannot be solved by integer grouping.
Reason: For a = 1 you need two numbers that multiply to c and add to b.
- x^2 + 10x + 21: 3 and 7 multiply to 21 and add to 10, so factor as (x + 3)(x + 7) = 0 → x = −3, −7.
- The other three have no pair of integers whose product is c and sum is b, so they cannot be solved by integer grouping.
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