Maths Question Help

Hey guys,
Do you also mind helping me with question 10? I got k>-9 but why must both roots be positive and how do I arrive at k<0? Thank you

(edited 2 years ago)

image.jpg514.1KB

image.jpg448.9KB

Reply 1

grhas98

The roots must be positive because you are doing the quadratic equation to find t^2 which has to be positive,

So 6 - root(36 + 4k) > 0 must hold meaning that k < 0 if you rearrange

Reply 2

Nithu05

Original post by grhas98

The roots must be positive because you are doing the quadratic equation to find t^2 which has to be positive,

So 6 - root(36 + 4k) > 0 must hold meaning that k < 0 if you rearrange

Thanks so much! But where do they get 6-root(36+4k) from?

Reply 3

mqb2766

Original post by Nithu05

Thanks so much! But where do they get 6-root(36+4k) from?

Last line of the frist part, so solving the quadratic
x^2 - 6x - k = 0
The bold is (double) the smallest root which must be positive.

Reply 4

Nithu05

Original post by mqb2766

Last line of the frist part, so solving the quadratic
x^2 - 6x - k = 0
The bold is (double) the smallest root which must be positive.

Just to confirm they used the quadratic formula and set the numerator>0. Is the reason they didn't use the 6+root36+4k because it is already positive as established by the fact that k>-9?

(edited 2 years ago)

Reply 5

mqb2766

Original post by Nithu05

Just to confirm they used the quadratic formula and set the numerator>0. Is the reason they didn't use the 6+root36+4k because it is already positive as established by the fact that k>-9?