Question

TOUGH ONE!!! The value of p for which the roots of the quadratic equation 4x^2-20px+(25p^2+15p-66)=0 are less than 2 ,lies in interval .......................

Answer 1

Oh there's some fun algebra here... :)

Ultimately this is a quadratic equation:
\[ax^2 + bx + c = 0\]
Where
\[a = 4 \qquad b = -20p \qquad c = 25p^2+15p-66\]
Now you have to use the quadratic formula to find out where the roots are less than 2.

Let me try to cook up a geogebra file to visualize this.

Answer 2

show me

Answer 3

c = OMG

Answer 4

wat?

Answer 5

nvm

Answer 6

I've attached a geogebra file which illustrates this. It doesn't give an exact solution of course, but hopefully it lends some intuition to the problem. :)

Answer 7

its not working
plz give algebraic answer

Answer 8

Wait, let me....

Answer 9

You need geogebra to open it. http://www.geogebra.org/ and click installers. It's well worth it. :)

Answer 10

Arivand, did my hint help? How far have you gotten with this problem so far? I will better be able to help this way.

Answer 11

plz give algebraic answer

Answer 12

{x = 3 / 4, x = (-3) / 4}

Answer 13

I used geogebra and found that solution. mathteacher, you could have used CAS on Geogebra to find it

Answer 14

Arivind, I am happy to help you work through the problem, but I don't just give solutions without any student input. There is no learning that way. :)

Answer 15

plz give steps

Answer 16

4x^2-20px+(25p^2+15p-66)=0

here , we use quadratic equation

where , a =4
b= -20p
and, c = (25p^2+15p-66)

Answer 17

thn............

Answer 18

how?

Answer 19

You should be happy you have the solutions. You can use the quadratic formula instead

Answer 20

now sum of roots is
\[\alpha +\beta=-(-20p)/4\]

Answer 21

so.............

Answer 22

\[\alpha +\beta=5p\]

Answer 23

\[\alpha \times \beta= c/a\]

Answer 24

................
lead me to answer