Question
π§2 + 6π§ + 25 = 0 and Express the solutions in the form π + ππ.
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Answer to a math question π§2 + 6π§ + 25 = 0 and Express the solutions in the form π + ππ.
Fred
4.4115 Answers
Solution:
1. Identify the coefficients in the quadratic equationz^2 + 6z + 25 = 0
-a = 1 b = 6 c = 25
2. Use the quadratic formulaz = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
3. Calculate the discriminantb^2 - 4ac
-b^2 = 6^2 = 36
-4ac = 4 \times 1 \times 25 = 100
- Discriminant:b^2 - 4ac = 36 - 100 = -64
4. Substitute back into the quadratic formula:
z = \frac{-6 \pm \sqrt{-64}}{2 \cdot 1}
5. Simplify:
- The square root of-64 8i \sqrt{-64} = 8i
- Therefore,z = \frac{-6 \pm 8i}{2}
6. Split the expression for each solution:
-z_1 = \frac{-6 + 8i}{2} = -3 + 4i
-z_2 = \frac{-6 - 8i}{2} = -3 - 4i
7. The solutions in the forma + bi
-z_1 = -3 + 4i
-z_2 = -3 - 4i
1. Identify the coefficients in the quadratic equation
-
2. Use the quadratic formula
3. Calculate the discriminant
-
-
- Discriminant:
4. Substitute back into the quadratic formula:
5. Simplify:
- The square root of
- Therefore,
6. Split the expression for each solution:
-
-
7. The solutions in the form
-
-
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