MYTUTOR SUBJECT ANSWERS

415 views

If (m+8)(x^2)+m=7-8x has two real roots show that (m+9)(m-8)<0 where m is an arbitrary constant

For this we are going to test our knowledge of discriminats and factorisation.
Firstly we will format the equation as (m+8)x2+8x+(m-7)=0

From here we can see it takes the form ax2+bx+c, and as we know the equation has two real roots we know that the discriminant D is greater than 0. Therfore b2-4ac>0

a=(m+8)        b=8          c=(m-7)

82-4(m+8)(m-7)>0       Pluggin in a,b,c

64-4(m2+m-54)>0       expanding brackets and squaring 8

16-(m2+m-54)>0         dividing both sides by a factor of 4

0>(m2+m-54)-16         moving left handside to right handside by addition / subtraction

0>m2+m-72                 collecting terms

0>(m+9)(m-8)             factorising

We have now shown that (m+9)(m-8)<0 for the above equation when it has two real roots.

Marcus J. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathema...

1 year ago

Answered by Marcus, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

295 SUBJECT SPECIALISTS

£22 /hr

Jay L.

Degree: Computer Science (Masters) - Bristol University

Subjects offered:Maths, Computing+ 1 more

Maths
Computing
Chemistry

“About me: Hi, I’m Jay, a first year Computer Science student at the University of Bristol! I am here to help students prepare for their exams (GCSE, AS/A Level etc) in Maths and Computing. My teaching style can vary depending on how y...”

£20 /hr

Evelin H.

Degree: Economics (Bachelors) - Durham University

Subjects offered:Maths, Economics+ 1 more

Maths
Economics
-Personal Statements-

“Hi! I’m Evelin, an undergraduate at Durham University. Having been a tutor before, I know how hard it can be to keep up with all the work. So why do it alone?”

£24 /hr

Prina S.

Degree: Environmental Geoscience (Masters) - Bristol University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Geography
Biology

“Hello there! My name is Prina and I'm a first year Environmental Geoscience at the University of Bristol. My love for science was instilled in me by those who taught me and I hope to share my passion in the same way through exciting an...”

About the author

£20 /hr

Marcus J.

Degree: Mathematics (Masters) - Exeter University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I'm a high achieving Master of Mathematics student at Exeter. With an excitement for my subject and 7 years tutoring experience, at many academic levels.”

MyTutor guarantee

You may also like...

Posts by Marcus

How do we differentiate y=a^x when 'a' is an non zero real number

If (m+8)(x^2)+m=7-8x has two real roots show that (m+9)(m-8)<0 where m is an arbitrary constant

Other A Level Maths questions

What is the method used for differentiation?

A Definitive Guide to Differentiation

A curve has equation y = 2x^5 + 5x^4 1 . (a) Find: (i) dy/ dx [2 marks] (ii) d^2y/ dx^2 (b) The point on the curve where x ¼ 1 is P. (i) Determine whether y is increasing or decreasing at P, giving a reason for your answer.

The points P (2,3.6) and Q(2.2,2.4) lie on the curve y=f(x) . Use P and Q to estimate the gradient of the curve at the point where x=2 .

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok