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determine the standard form of the quadratic equation given the following sum and the product roots.

1. sum = 2, product = -3?
2. sum = 0, product= -16?
3. sum= 7, product = 0?
4. sum =2/3, product = 5/3?
5. sum = -4/5, product = 3/2? ​

Sagot :

Answer:

Apply this to the given sums and products.

1. Sum = 2, Product = -3

Using the formulas:

[tex]z^2 - (\text{sum})z + (\text{product}) = 0[/tex]

[tex]z^2 - 2z - 3 = 0[/tex]

2. Sum = 0, Product = -16

[tex]z^2 - (\text{sum})z + (\text{product}) = 0[/tex]

[tex]z^2 - 0z - 16 = 0[/tex]

[tex]z^2 - 16 = 0[/tex]

3. Sum = 7, Product = 0

[tex]z^2 - (\text{sum})z + (\text{product}) = 0[/tex]

[tex]z^2 - 7z + 0 = 0[/tex]

[tex]z^2 - 7z = 0[/tex]

[tex]{4. Sum = \(\frac{2}{3}\), Product = \(\frac{5}{3}\)

\[ z^2 - \left(\frac{2}{3}\right)z + \left(\frac{5}{3}\right) = 0} [/tex]

[tex]5. Sum = \(-\frac{4}{5}\), Product = \(\frac{3}{2}\)[/tex]

[tex]z^2 - \left(-\frac{4}{5}\right)z + \left(\frac{3}{2}\right) = 0[/tex]

[tex]z^2 + \frac{4}{5}z + \frac{3}{2} = 0[/tex]