Question

Find the zeroes of the quadratic polynomial 9x2 – 6x + 1 and verify the relationship between the zeroes and the coefficients.

Answer 1

Answer:

zeros of the quadratic polynomial is 1/ 3 and 1/ 3

Step-by-step explanation:

9x^2 -6x +1

9x^2 -3x -3x +1

3x (3x-1 )-1 (3x-1 )

(3x-1 )(3x-1 )

x= 1/3 and 1/3

Answer 2

Given:

9x²-6x+1=0

To Find:

1) Zeros of the given quadratic polynomial

2) To verify the relationship between the zeroes and the coefficients.

Solution:

9x²-6x+1=0......(Given)

9x²-3x-3x+1=0

3x(3x-1) -1(3x-1) =0

(3x-1) (3x-1) =0

(3x-1) =0 OR (3x-1) =0

3x=1 OR 3x=1

x=1/3 OR x=1/3

(1/3, 1/3) are the zeroes of the given quadratic polynomial.

Now, Put x=1/3 in the quadratic polynomial to verify the relationship between the zeroes and the coefficients.

9x²-6x+1=0

9(1/3) ²-6(1/3) +1=0

9(1/9/-6/3+1=0

1-2+1=0

-1+1=0

0=0

So this roots are real and equal.