Expert: Steve Holleran - 2/28/2007

Question
Please help me solve these..if you can.

choose a value for k so that the equation

5x^2-10x+7=k

has no real roots.Use the quadratic formula to prove that this equation has no
real roots for your choosen value for k.


PLEASE PLEASE PLEASE AND IF U KNOW WHO CAN...PLEASE

Answer
Hi Pearl,

Okay, this should not be too tough.

Remember in the quadratic formula, the part thats under the square root (called the discriminant) is b^2 - 4ac.

If this result is < 0 , then the equation has no real roots because the formula then has a negative number under a square root sign.  So we want b^2 - 4ac < 0

First, though, we have to get your equation = 0 , so subtract the k  and get :

5x^2 - 10x + (7-k) = 0

Now, a = 5, b = -10 and c = 7-k  so you get

b^2 - 4ac < 0 means (-10)^2 - 4(5)(7-k) < 0

               or   100 - 20 ( 7-k) < 0

               or   100 - 140 + 20k < 0

               or       -40 + 20k < 0

               so that  20k < 40  and k < 2.

So, any value less than 2 will work.  Okay, lets choose 1:

5x^2 - 10x + 7 = 1 so that 5x^2 - 10x + 6 = 0

Now b^2 -4ac = 100 - 4(5)(6) = 100 - 120 = -20 < 0 so the equation has no real roots.

Hope this helps you out.

Steve Holleran