The value of b is 14
The value of c is 65
Step-by-step explanation:
The quadratic equation ax² - bx + c = 0, where a = 1 has two roots
∵ The quadratic function is g(x) = ax² + bx + c
∵ a = 1
∴ g(x) = x² + bx + c
∵ g(x) has two complex roots (-7 + 4i) and (-7 - 4i)
∴ g(x) = 0
∴ x² + bx + c = 0
∵ The general form of the quadratic equation is x² - bx + c = 0,
with sum of roots b and product of roots c
- Compare them
∴ x² - (-b) + c = 0
∵ -b = the sum of the two roots
∴ -b = (-7 + 4i) + (-7 - 4i)
- Add like terms
∴ -b = (-7 + -7) + (4i + -4i)
∴ -b = -14 + 0
∴ -b = -14
- Multiply both sides by -1
∴ b = 14
The value of b is 14
∵ c is the product of the two roots
∴ c = (-7 + 4i)(-7 - 4i)
- Remember (a + b)(a - b) = a² - b²
∵ (-7 + 4i)(-7 - 4i) = (-7)² - (4i)²
∵ (-7)² = 49
∵ (4i)² = 16i²
∵ i² = -1
∴ (4i)² = -16
∴ (-7)² - (4i)² = 49 - (-16) = 49 + 16 = 65
∴ (-7 + 4i)(-7 - 4i) = 65
∴ c = 65
The value of c is 65
Learn more:
You can learn more about the quadratic equation in brainly.com/question/1357167
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