Maths homework. Need urgent help
How do I solve the equation 5x^2 + 3x + 4 = 0, I would like this answered ASAP
there's a rule you have to learn :
ax2 + bx + c = 0
1st : calculate a strange quantity : b2 - 4ac
2nd : if This quantity is positive then
x = (-b + sqrt(quantity)) / 2a
or
x = (-b - sqrt(quantity)) / 2a
your example :
quantity = 3x3 - 4x5x4 = -71
Two possibilities : no solution OR complex solution
If you've seen complexes : -71 = 71 x i x i... then you go on has explained but with the quantity beeing equal to sqrt(71)xi
x = (-3 + ixsqrt(71)) / 10
or
x = (-3 - ixsqrt(71)) / 10
5x^2 + 3x + 4 = 0
Answer, the Quadratic equation. Now, don’t freak out if you don’t know what that is, or if you see how long this is. I pressed enter a lot. Like the other person said,
b^2-4ac, but, there is more! We’ll cover the rest after we deal with b^2-4ac.
Doesn’t make sense? Here I show you how to label the question. It goes alphabetically, from a, to b, to c.
5x^2 + 3x + 4 = 0
A B C
5x^2 is a, 3x is b, and 4 is c.
Now you put it in the equation.
(3)^2-4(5)(4)
First, 3 squared, or 3 to the second power, is easy! 3*3=9!
So, we have 9-4(5)(4)
The second step is 4*5, or 5*4, or 4*4. Lets' go with 5*4. 20.
Now, Multiply it by the other 4. 20*4. Just like 2*4, and then add a 0 to the result! 80!
Now we have 9-80. Ugh, I don’t like negative numbers. (How about you?)
9-80 is -71, and now we can move on to the next part. Like I said, we are solving this using the Quadratic Equation, and the full Equation is.....
-b±(√b^2-4ac)/2a
Since -71 is a negative number, you have 2 imaginary solutions, because we cannot find the square root of a negative number. -71/2a (2a=10, since a=5 in this problem) is what you need.
You now have 2 imaginary answers, exactly what you need.
√-71, divided by 10, +-3
√-71, divided by 10, - -3
Those are the answers, and you cannot simplify them more, unless you can find the square root of a negative number. Minus negative three equals plus positive 3 by the way.
ax^2bx+c=0
a=5 b=3 c=4
x= -b±√b^2-4ac÷2a (formula)
x= -3±√-71÷10 (ans)
hear √b^2-4ac=D (value of x depend upon d)
the answer is not in real number because d<0
the answer also can be written in from of
-3 (71i)÷10 (I=irrational number)
X rise to the power 2 minus X minus 6=0
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