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