#### Using "Bounds on Zeros", where would we find the real roots of this function?

10x^{3} -6x^{2} +4x = 3

Anonymous

0

10x^{3} -6x^{2} +4x = 3

Sangeetha Pulapaka

0

STEP 1: Recall what are polynomials

https://www.youtube.com/watch?v=ffLLmV4mZwU

STEP 2: Recall what are the zeros of a polynomial

https://www.mathstips.com/zeroes-of-polynomial/

STEP 3: Recall what are "bounds on zeros"

https://www.mathsisfun.com/algebra/polynomials-bounds-zeros.html

STEP 4: Calculate the bounds on zeros of the given polynomial.

The leading coefficient is 10, so we must divide all terms by 10

10 x^{3} - 6x^{2} + 4x - 3

The coefficients are: 1, -0.6, 0.4 and -0.3

Drop the leading coefficient, and remove any minus signs: 0.6, 0.4, 0.3

• Bound 1: the largest value is 0.6. Plus 1 = **1.6**

• Bound 2: adding all values is: 0.6 + 0.4 + 0.3 = 1.3 which is MORE than 1, so the answer is **1**

The smallest bounds value is **1.6**

Therefore all real roots will lie between -1 and +1