Here we're presented with a quadratic equation which needs to be expanded and then rewritten in descending powers of x:
1x^2 + m^2x^2 + 6mx + 9 - 3 = 0.
Let's group like terms: 1x^2 + m^2x^2 + 6mx + 6 = 0.
The first 2 terms can be rewritten as a single term: (1+m^2)x^2, and so we now have:
(1+m^2)x^2 + 6mx + 6 = 0.
We must now calculate the discriminant and set the resulting expression = to 0, as a preliminary to finding the value of m for which the given quadratic has equal roots:
discriminant: (6m)^2 - 4(1+m^2)(6) = 0
Then 36m^2 - 24(1+m^2) = 0, which simplifies to 12m^2 - 24 = 0.
Then 12 m^2 = 24; m^2 = 2, and m = √2.
When the discriminant is zero, as it is here when m = √2, then the given quadratic has two equal roots.
Answer:
what are the choices
Step-by-step explanation:
Answer:
no
Step-by-step explanation:
The given lengths do not satisfy the Pythagorean theorem:
34² ≠ 33² +16²
1156 ≠ 1089 +256
The given sides do not form a right triangle.
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<em>Alternate solution</em>
You can also compute 34² -33² = (34+33)(34-33) = 67·1 = 67 ≠ 16².
Even simpler, a Pythagorean triple will never have zero or two even numbers. The numbers (16, 33, 34) cannot be a Pythagorean triple.
Answer:
well then you fail and thats that
Step-by-step explanation: