# Help!!! Wjec as sam maths unit 1 question 9

Watch
#1
1 3 minutes ago Report post
9) The quadratic equation 4x^2 􏰅- 12x􏰈 + m =􏰆0, where m is a positive constant, has two distinct real roots.
Show that the quadratic equation3x^2 􏰈+mx +􏰈7􏰆= 0 has no real roots.

I know how to the first quadratic equation but when I looked at the answer for second quadratic equation.

b2 –4ac=m^2 –84
m2 <81 ---> 􏰂b2 –4ac<–3
b2 –4ac<0􏰂 ---> no real roots
Where did 81 come from???
0
2 years ago
#2
(Original post by Raaheel)
1 3 minutes ago Report post
9) The quadratic equation 4x^2 􏰅- 12x􏰈 + m =􏰆0, where m is a positive constant, has two distinct real roots.
Show that the quadratic equation3x^2 􏰈+mx +􏰈7􏰆= 0 has no real roots.

I know how to the first quadratic equation but when I looked at the answer for second quadratic equation.

b2 –4ac=m^2 –84
m2 <81 ---> 􏰂b2 –4ac<–3
b2 –4ac<0􏰂 ---> no real roots
Where did 81 come from???
Since the first quadratic has two distinct real roots, we have (-12)^2 > 4(4)(m), i.e. m < 9. Since m is given to be positive, and 9 is certainly positive, we know that both sides of this inequality are positive, so we can safely square both sides to give m^2 < 81 (note that e.g. if one side is negative, then we can't necessarily square, e.g. -5 < 3 is true, but then squaring both sides gives 25 < 9 which is false. That is why we had to make sure that both sides were positive before squaring.)
0
#3
(Original post by Prasiortle)
Since the first quadratic has two distinct real roots, we have (-12)^2 > 4(4)(m), i.e. m < 9. Since m is given to be positive, and 9 is certainly positive, we know that both sides of this inequality are positive, so we can safely square both sides to give m^2 < 81 (note that e.g. if one side is negative, then we can't necessarily square, e.g. -5 < 3 is true, but then squaring both sides gives 25 < 9 which is false. That is why we had to make sure that both sides were positive before squaring.)
Thank you so much
Then you use same value for m for the second quadratic equation and why?. I thought m is different in each case
0
2 years ago
#4
(Original post by Raaheel)
Thank you so much
Then you use same value for m for the second quadratic equation and why?. I thought m is different in each case
If they were different, the problem author would have used different letters, as otherwise the problem would be ambiguous. When you see a question that uses the same variable multiple times, you can be certain that they are referring to the same thing.
0
#5
(Original post by Prasiortle)
If they were different, the problem author would have used different letters, as otherwise the problem would be ambiguous. When you see a question that uses the same variable multiple times, you can be certain that they are referring to the same thing.
Thank you so much, I was trying to figure that question for ages. Thank you
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### What are you most likely to do if you don't get the grades you were expecting?

Go through Clearing (251)
39.72%
Take autumn exams (187)
29.59%
Look for a job (21)
3.32%
Consider an apprenticeship (25)
3.96%
Take a year out (110)
17.41%
Something else (let us know in the thread!) (38)
6.01%