Question

Remember the quadratic formula? Given ax²+bx+c=0, the solution is x=(-b±√(b^2-4ac))/(2a), which may have felt arduous to memorize in high school, but you have to admit is a conveniently closed-form solution.

Now, if we go up to ax³+bx²+cx+d=0, a closed form for “x=” is possible to find, although it’s much bulkier than the quadratic version. It’s also possible, yet ugly, to do this for degree 4 polynomials ax⁴+bx³+cx²+dx+f=0.

Answer 1

Answer:

Do u know the answer................ ma'am

Answer 2

Answer:

Now we just need to rearrange the equation to leave "x" on the left

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

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

Move b/2a to right x = -b/2a (+-) sqrt(-c/a+(b/2a)^2)

That is actually solved! But let's simplify it a bit:

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

Simplify: x = [ -b (+-) sqrt(-4ac + b^2) ] / 2a

Which is the Quadratic formula we all know and love:

Quadratic Formula: x = [ -b (+-) sqrt(b^2 - 4ac) ] / 2a

Step-by-step explanation:

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