How to use the discriminant to find out how many real number roots an equation has for $14a^2 - a= 5a^2 - 5a$ ?

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How to use the discriminant to find out how many real number roots an equation has for $14a^2 - a= 5a^2 - 5a$ ?

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Answer 1 · 2015-05-18T00:14:53

Write it collecting all terms to the left as in:
$14a^2-a-5a^2+5a=0$
$9a^2+4a=0$

This is in the form:
$ma^2+na+p=0$
where:
$m=9$
$n=4$
$p=0$
The discriminant is:
$Delta=n^2-4mp=16-4(9*0)=16>0$
Your equation will give you 2 real distict solutions.
[In this case $x_1=0 and x_2=-4/9$ ]

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How to use the discriminant to find out how many real number roots an equation has for $14a^2 - a= 5a^2 - 5a$ ?

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How to use the discriminant to find out how many real number roots an equation has for 14a^2 - a= 5a^2 - 5a14a^2 - a= 5a^2 - 5a?

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How to use the discriminant to find out how many real number roots an equation has for $14a^2 - a= 5a^2 - 5a$ ?