MYTUTOR SUBJECT ANSWERS

566 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

306 SUBJECT SPECIALISTS

£24 /hr

Ed W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
Chemistry
Biology
-Medical School Preparation-

“Hi! I'm Ed and I'm currently studying Medicine at the University of Edinburgh. I tutor at GCSE and A Level forBiology, Chemistry and Maths, and at GCSE level forFurther Maths. These are subjects I'm very comfortable in and enjoy. With ...”

£24 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£26 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

About the author

Marcus J.

Currently unavailable: for regular students

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

How do I differentiate y = (3 + 6x)^5 with respect to x

How to translate a function of form y = f(x)

Given x = 3tan(2y) find dy/dx in terms of x

A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

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