Q- how much smaller than 2a+4b-c is 5a -3b +2c
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Answers
Step-by-step explanation:
ax
2
+bx+c=0, where a
=0.
Condition for real roots of a quadratic equation is b
2
≥4ac. This condition has
to be true. As for the second condition to be true, all coefficient should be
positive.
The proof is easy. If you know a little calculus then you can find that a quadratic
function reaches its extremum when x=
2a
−b
. This result can be derived via
rearranging the terms in the form of a(x+p)
2
+q. Also we know that the
extremum is always halfway between the two roots. So when both of the roots
are negative then the extremum should also be negative.
−
2a
b
<0
or,
a
b
>0
or,
a
2
ab
>0
or, ab>0.
So both a and b should have same sign. Without loss of generality it would be
safe to assume that both a and b is positive (if they were negative then multiply
the quadratic by (-1)). The general from of the roots are
x=
2a
−b±
b
2
−4ac