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 ...
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.
41th
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.