David W. answered • 10/05/16
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(90)
Experienced Prof
x2 +1.5x-10 is an expression.
When written like this:
x2 +1.5x-10 = 0
it becomes an equation. And, since it has the form:
ax2 + bx + c (x is a variable; a,b,c are constants)
it is a quadratic equation and may be solved (that is, the value of x may be found) by using the quadratic formula:
x = ( -b ± √(b2-4ac) )/2a
Your teacher is trying to point out that using the quadratic formula with b=1.5 is a little bit harder than using the quadratic formula with b=3 (for example, to square b).
So, when you multiply 0 by 2, you get 0 and the equation becomes:
2x2 + 3x - 20 = 0
which has the same value of x for a solution (the value(s) of x for which the equation is true].
Now, you may solve for x using the quadratic formula with both sets of (a.b.c) values to see if you get the same solution.
Andrew M.
As I put in my answer:
If a=b
then ax = bx
Example: 7-4=3
2(7-4)=2(3)
Think of the linear equation x=4
If we multiply both sides by 2 and
change this to 2x=8 it is the
same line when graphed.
Look at a simple quadratic:
x2+4x+3=0
This factors to
(x+3)(x+1) =0
x=-3 or x=-1
Multiply through by 2
2x2+8x+6=0
(2x2+6x)+(2x+6)=0
2x(x+3)+2(x+3)=0
(2x+2)(x+3)=0
x=-1 or x=-3
Same answer because we kept all
terms in the same proportion to each other.
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10/05/16
Pooja B.
So we can multiply the expression by any number as long as we get a whole number in the middle and everything is in proportion to each other. its the absolute same value?
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10/05/16
Andrew M.
x = x multiply through by some value 'a'
ax = ax. divide both sides by 'a'
x = x equation is not actually changed
As long as you multiply everything on both
sides by the same value, it will divide back
out in the end without changing the value of x.
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10/05/16
Pooja B.
10/05/16