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USPshnik [31]
2 years ago
11

Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.

Mathematics
1 answer:
vlabodo [156]2 years ago
4 0

Answer:

Real numbers = 39 and 9

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0

Given the following data;

a = 1

b = -43

c = 306

Quadratic equation formula is;

x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a}

Substituting into the equation, we have;

x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1}

x = \frac {43 \pm \sqrt {1849 - 1224}}{2}

x = \frac {43 \pm \sqrt {625}}{2}

x = \frac {43 \pm 25}{2}

x_{1} = \frac {43 + 25}{2}

x_{1} = \frac {68}{2}

x_{1} = 39

x_{2} = \frac {43 - 25}{2}

x_{2} = \frac {18}{2}

x_{2} = 9

Therefore, the two real numbers are 39 and 9.

The quadratic equation now becomes;

x² - 43x + 306 = (x - 39)(x - 9) = 0

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