Question

Find zeroes of polynomial: p(x) = x²/3 - 4x + 7/3( without using quadratic formula)​

Answer 1

Step-by-step explanation:

Given:-

A polynomial p(x)=x²/3-4x+7/3

To find:-

Find zeroes of polynomial: p(x) = x²/3 - 4x + 7/3( without using quadratic formula).

Solution:-

Given polynomial p(x)=x²/3-4x+7/3

=>(x²-12x+7)/3

To get the zeroes of the polynomial we equate with zero.

=>(x²-12x+7)/3=0.

Completing the square method:

=>x²-12x+7=0

=>x²-12x=-7

=>x²-2(x)(6)=-7

On adding 6² both sides,then

=>x²-2(x)(6)+6²=-7+6²

=>x²-2(x)(6)+6²=-7+36

LHS is in the form of a²-2ab+b²

a²-2ab+b²=(a-b)²

=>(x-6)²=29

=>x-6=±√29

=>x=6±√29

x =6+√29 and 6-√29

Answer:-

Zeroes of the polynomial p(x)=x²/3-4x+7/3 are 6+√29 and 6-√29

Used concept:-

To get zeroes for the given quadratic polynomial we use,

• Factorization method
• Quadratic formula method
• Completing the square method.