Question

Find the zeros of the quadratic polynomial 9y2-6y +1and verify the relationship between the zeroes and the coefficients.

Answer 1

Answer:

$54xy \frac{0 \sqrt{02222y2y2 \frac{2 \frac{?}{?} }{?} \times \frac{?}{?} } }{?}$

Answer 2

Answer:

y=1/3

Step-by-step explanation:

Here, the given Quadratic polynomial is

p(x) =9y²-6y+1

Let, p(x) =0

=>9y²-6y+1=0

=> Using this formula,

(Alpha,Beta) = -b±√D /2a

D=√b²-4ac =√(-6)²-4(9)(1) =√36-36 =0

Now,

Alpha= -b+√D /2a = -(-6)+√(0) /2(9) = 6/18 = 1/3

Beta= -b-√D /2a = -(-6)-√(0) /2(9) = 6/18 = 1/3

we get, (Alpha,Beta)=(1/3, 1/3)

We take,

p(1/3)=9(1/3)²-6(1/3)+1 =9(1/9)-6(1/3)+1 = 1-2+1 =0

=>Alpha×Beta = c/a

=>(1/3)×(1/3) = 1/9

=> 1/9 = 1/9

=>Alpha+Beta = -b/a

=>(1/3)+(1/3) = -(-6)/9

=> 2/3 = 2/3