Question

Solve the following equations.

X^2 + 5x + 6 = 0
(Factorise)

X^2 + 7x + 11 = 0
(Use the quadratic formula)

Answer 1

facotr
ax^2+bx+c=0
find what 2 number multiply to c and add to b
what 2 numbers multiply to 6 and add to 5
2 and 3
(x+2)(x+3)=0
set to zero
x+2=0
x=-2
x+3=0
x=-3
x=-2 or -3



other one
for ax^2+bx+c=0
x=
`\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}`

we are given
x^2+7x+11=0
a=1
b=7
c=11

sub
x=
`\frac{-7+/- \sqrt{7^(2)-4(1)(11)} }{2(1)}`
x=
`(-7+/- √(49-44) )/(2)`
x=
`(-7+/- √(5) )/(2)`
x=
`(-7+ √(5) )/(2)` or
`(-7- √(5) )/(2)`