Show that the equation has real roots for all values of a are real numbers ..

I tried this ..

Is it because is a quadratic equation and hence it has real roots ? Or i am in the wrong path ...

Printable View

- Jan 11th 2009, 02:53 AMmathaddictReal roots
Show that the equation has real roots for all values of a are real numbers ..

I tried this ..

Is it because is a quadratic equation and hence it has real roots ? Or i am in the wrong path ... - Jan 11th 2009, 03:04 AMMoo
Hello,

In order to prove that the first equation (x²+(3a-2)x+a(a-1)=0) has real roots, you have to prove that the discriminant, 5a²-8a+4 is always positive (or equal to 0).

So you have to see when

In order to prove this, find the discriminant : 64-16*5<0

Hence the sign of 5a²-8a+4 is always the same, and its sign is the sign of the leading coefficient, 5.

Thus for all a.

Therefore, the equation has real roots for all a.

41:):)th - Jan 11th 2009, 03:06 AMhmmmm
you would have to show that the descriminant is always greater or equal zero for a as real number, so you would have to show that 5a^2-8a+4 is always greater than or equal to zero. You could do this by plotting the function on a graph.

sorry for repeating what was just said i think i posted it at the same time.