1. derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
2. divide all terms in the equation by a.
3. subtract the constant (the term without an x) from both sides.
4. add a constant (in terms of a and b) that will complete the square.
5. take the square root of both sides of the equation.
6. solve for x.

We are given that:

a x^2 + b x + c = 0

Divide all terms with c/ a:

x^2 + (b / a) x + (c / a) = 0

Subtract c from both sides:

x^2 + (b / a) x + (c / a) – c / a = 0 – c / a

x^2 + (b / a) x = - c / a

Add a constant k to complete the square:

where k = ((b / a) / 2)^2 = (b /2a)^2

x^2 + (b / a) x  + k = - c / a + k

x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2

So the perfect square trinomial is:

(x + b/2a)^2 = - c / a + (b /2a)^2

Taking the square root of both sides:

x + b/2a = sqrt [- c / a + (b /2a)^2]

x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)

step-by-step explanation:

quartic functions has x = –1 and x = –2 as its only two real zeroes:

f(x) = a(x+2)(x+1)   a: real number

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.