MYTUTOR SUBJECT ANSWERS

574 views

How many distinct real roots does the equation x^3 − 30x^2 + 108x − 104 = 0 have?

We can see that 104 = 2^3 * 13 = 2*2*26, 30 = 2 + 2 + 26, and 108 = 2*2 + 2*26 + 2*26, so the coefficients agree with the Vieta's formulas, so the roots of the equation above are 2, 2, 26. In conclusion, it has 2 distinct real roots. 

Alternatively, we can try to factorise the polynomial. This can be done by (x-2)^2*(x-26), and so we can see that the equation has 2 distinct real roots. 

Andreea I. Uni Admissions Test .MAT. tutor, Uni Admissions Test .STEP...

1 year ago

Answered by Andreea, an Uni Admissions Test .MAT. tutor with MyTutor


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

14 SUBJECT SPECIALISTS

£36 /hr

Joe B.

Degree: Mathematics G100 (Bachelors) - Bath University

Subjects offered:.MAT., Maths+ 4 more

.MAT.
Maths
Further Mathematics
Economics
.STEP.
-Personal Statements-

“About Me Hi, I'm Joe, a first year mathematics student from Luton studying at Bath University. I am an accomplished mathematician and economist, having achieved A* grades in A Level Maths, Further Maths and Economics in June 2016. As ...”

£25 /hr

Valerio C.

Degree: Mathematics (MMath) (Bachelors) - Oxford, Exeter College University

Subjects offered:.MAT., Maths+ 2 more

.MAT.
Maths
Further Mathematics
-Oxbridge Preparation-

“Maths student at Oxford, tennis player, cook. My secret is to teach students how to think mathematically.”

MyTutor guarantee

£25 /hr

Killian D.

Degree: Mathematics (Bachelors) - Edinburgh University

Subjects offered:.MAT., Physics+ 1 more

.MAT.
Physics
Maths

“Who am I? I am a first year Mathematics student in the University of Edinburgh. I am studying full time but have chosen to tutor as well as I have a passion for the subject; something I believe you will discover for yourself in our tu...”

About the author

£25 /hr

Andreea I.

Degree: Mathematics and Computer Science (Masters) - Oxford, Merton College University

Subjects offered:.MAT., Maths+ 1 more

.MAT.
Maths
.STEP.

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

MyTutor guarantee

You may also like...

Posts by Andreea

By use of calculus, show that x − ln(1 + x) is positive for all positive x.

How many distinct real roots does the equation x^3 − 30x^2 + 108x − 104 = 0 have?

The quadratic equation 2x^2 + 8x + 1 = 0 has roots a and b. Write down the value of a + b, a*b and a^2 + b^2.

Other Uni Admissions Test .MAT. questions

The inequality x^4 < 8x^2 + 9 is satisfied precisely when...

Circle the correct letter: The equation x^3 - 30x^2 + 108x - 104 = 0 has a) No real roots; b) Exactly one real root; c) Three distinct real roots; d) A repeated root.

When is the inequality x^4 < 8x^2 + 9 true?

The sequence xn is given by the formula x_n = n^3 − 9n^2 + 631. What is the largest value of n for which x_n > x_(n+1)?

View Uni Admissions Test .MAT. 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