Question

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

Answer 1

Answer:

$4x^2+72x+259=0$

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

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