Question

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

Answer 1

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

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+(√(65))/(2)\\ \\x_1=-9-(√(65))/(2)`

Then the equation is

`\left(x-\left(-9+(√(65))/(2)\right)\right) \left(x-\left(-9-(√(65))/(2)\right)\right)=0\\ \\\left(x+9-(√(65))/(2)\right)\left(x+9+(√(65))/(2)\right)=0\\ \\x^2+9x+(√(65))/(2)x+9x+81+(9√(65))/(2)-(√(65))/(2)x-(9√(65))/(2)-(65)/(4)=0\\ \\x^2+18x+(259)/(4)=0\\ \\4x^2+72x+259=0`