quadratic equations: 3 - sqrt(14) and 3 + sqrt(14)

[janelle68]

I need help with these quadratic equations.

3-square root of 14 and 3+square root of 14

Also with 2-7i, 2+7i.

 

[Denis]

Re: quadratic equations

I need help with these quadratic equations. 3-square root of 14 and 3+square root of 14. Also with 2-7i, 2+7i.[/i][/code][/list]

Those are not quadratic equations; equations have equal signs, like x^2 + 3x - 10 = 0.
Post the original problem IN FULL.

 

[skeeter]

What you have given looks like zeros of a quadratic function.

If a quadratic function has two zeros a and b, then the following is true ...

k(x - a)(x - b) = 0, where k is a nonzero constant.

expanding the left side of the equation yields ...

k[x² - (a + b)x + ab] = 0

note that the linear coefficient is the opposite sum of the two zeros, and the constant term is the product of the two zeros.

for your first two zeros, \(\displaystyle 3 - \sqrt{14}\) and \(\displaystyle 3 + \sqrt{14}\), their sum is \(\displaystyle (3 - \sqrt{14}) + (3 + \sqrt{14}) = 6\).. so the coefficient of the linear term is -6.
the product is \(\displaystyle (3 - \sqrt{14})(3 + \sqrt{14}) = 9 - 14 = -5\), so the constant term is -5.

the resulting quadratic is y = k(x² - 6x - 5)

do the same procedure with the two zeros (2 - 7i) and (2 + 7i), remember that
i² = -1.