C1 quadratic equations with K help please!

I cant do any of the questions in exam papers about quadratic equations with K involved. :eek3:

And the exam is tomorow!
Can anyone help me with how they work please?
Here is one I cant do:

a, Simplify (k+5)^2 - 12K(K+2)

b, The quadratic equation 3(K+2)x^2+(K+5)x+k=0 has real roots.
i, Show that (K-1)(11K+25) <0 (Less than or equal to 0)
ii, Hence find possible values for K

Help please!!!

Reply 1

Tlc-X3

a) expand them both out
then try and simplify
so its:
k^2 + 10k + 25 - (12k^2 + 24k) <-- be careful about the minus!!

so k^2 + 10k + 25 - 12k^2 - 24k

-11k^2 - 14K + 25

Reply 2

insparato

15

a) Expand out.. and simplify

b) i) What can you do to find out about the roots of a quadratic equation ? Think about the inequality...

ii) Draw a sketch of the quadratic, for what values of k is (K-1)(11K+25) < 0 look at the graph.

Reply 3

avsmithy

lol i just did this question:

b) discriminant > 0
b^2-(4*a*c) > 0
sub in from the question and rearrange
tadaa!

ii) factorise and then draw a graph as you should always do with quadratic inequalities

Reply 4

George88

OP

Oh so do I use discriminant for b?

Reply 5

George88

OP

avsmithy

lol i just did this question:

b) discriminant > 0
b^2-(4*a*c) > 0
sub in from the question and rearrange
tadaa!

ii) factorise and then draw a graph as you should always do with quadratic inequalities