What is the quadratic equation if the solutions are -9+ √65 /2, -9- √65 /2

Answers

7

step-by-step explanation:

He gained 60,900 dollars for that land

4x^2+72x+259=0

Step-by-step explanation:

If x_1 and x_2 are the solutions to the quadratic equation, then this equation can be written as

(x-x_1)(x-x_2)=0

In your case,

x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}

Then the equation is

\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0

4x^2+72x+259=0

Step-by-step explanation:

If x_1 and x_2 are the solutions to the quadratic equation, then this equation can be written as

(x-x_1)(x-x_2)=0

In your case,

x_1=-9+\dfrac{\sqrt{65}}{2}\\ \\x_1=-9-\dfrac{\sqrt{65}}{2}

Then the equation is

\left(x-\left(-9+\dfrac{\sqrt{65}}{2}\right)\right) \left(x-\left(-9-\dfrac{\sqrt{65}}{2}\right)\right)=0\\ \\\left(x+9-\dfrac{\sqrt{65}}{2}\right)\left(x+9+\dfrac{\sqrt{65}}{2}\right)=0\\ \\x^2+9x+\dfrac{\sqrt{65}}{2}x+9x+81+\dfrac{9\sqrt{65}}{2}-\dfrac{\sqrt{65}}{2}x-\dfrac{9\sqrt{65}}{2}-\dfrac{65}{4}=0\\ \\x^2+18x+\dfrac{259}{4}=0\\ \\4x^2+72x+259=0



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