Question

How do you solve `x^2+8x+7=0`?

Answer 1

The solutions are
`color(blue)(x=-7,x=-1`

Explanation:

`x^2+8x+7=0`

The equation is of the form `color(blue)(ax^2+bx+c=0` where:
`a=1, b=8, c=7`

The Discriminant is given by:

`color(blue)(Delta=b^2-4*a*c`
`= (8)^2-(4* 1 * 7)`
`= 64 -28=36`

The solutions are found using the formula
`color(blue)(x=(-b+-sqrtDelta)/(2*a)`

`x = ((-8)+-sqrt(36))/(2*1) = ((-8+-6))/2`

`x=(-8-6)/2, color(blue)(x=-7`

`x=(-8+6)/2, color(blue)(x=-1`

Answer 2

Solve y = x^2 + 8x + 7 = 0

Ans: -1 and -7

Explanation:

Since (a - b + c = 0), use the shortcut. The 2 real roots are (- 1) and (-c/a = - 7).

Reminder of Shortcut :
a. When a + b + c = 0: 2 real roots: (1) and (c/a)
b. When (a - b + c ) = 0: 2 real roots: (-1) and (-c/a)
Remember this Shortcut. It will save you a lot of time and effort.