Question

Use the discriminant to find the number and type of solution for x^2+6x=-9​

Answer 1

D = 0; one real root

Explanation:

Discriminant Formula:

`\displaystyle \large{D = {b}^(2) - 4ac}`

First, arrange the expression or equation in ax^2+bx+c = 0.

`\displaystyle \large{ {x}^(2) + 6x = - 9}`

Add both sides by 9.

`\displaystyle \large{ {x}^(2) + 6x + 9 = - 9 + 9} \\ \displaystyle \large{ {x}^(2) + 6x + 9 = 0}`

Compare the coefficients so we can substitute in the formula.

`\displaystyle \large{a {x}^(2) + bx + c = {x}^(2) + 6x + 9 }`

• a = 1
• b = 6
• c = 9

Substitute a = 1, b = 6 and c = 9 in the formula.

`\displaystyle \large{D = {6}^(2) - 4(1)(9)} \\ \displaystyle \large{D = 36 - 36} \\ \displaystyle \large{D = 0}`

Since D = 0, the type of solution is one real root.