a-level maths help please?
a) solve the equation 4x^2+12x-0
f(x)=4x^2+12x+c
where c is a constant
b)given that f(x)=0, has equal roots, find the value of c and hence solve f(x)=0
thanks
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a.
You can not solve this as it is not an equation without an =, unless it is supposed to be '= 0', which is what I am assuming in this:
4x^2 + 12x = 0
4x(x + 3) = 0
4x = 0
x = 0
x + 3 = 0
x = -3
x = [-3, 0]
b.
f(x) = 4x^2 + 12x + c
f(0) = 4(0)^2 + 12(0) + c
f(0) = c
4x^2 + 12x + c = 0
ax^2 + bx + c = 0
a = 4
b = 12
c = ?
b = 2 * sqrt(ac)
b / 2 = sqrt(ac)
(b / 2)^2 = ac
(b / 2)^2 / a = c
(12 / 2)^2 / 4 = c
6^2 / 4 = c
36 / 4 = c
c = 9
4x^2 + 12x + 9 = 0
(2x + 3)(2x + 3) = 0
(2x + 3)^2 = 0