Question

find a quadratic polynomial whose zeros are 3 + root 5 divided by 5 and 3 minus root 5 / 5​

Answer 1

Answer:

25x { }^{2} - 30x + 4 = 025x

2

−30x+4=0

Step-by-step explanation

consider the zeroes be X

now

the first zero

x = \frac{3 + \sqrt{5} }{5}x=

5

3+

5

solving

5x - 3 - \sqrt{5} = 0.....(1)5x−3−

5

=0.....(1)

now the second zero

x = \frac{3 - \sqrt{5} }{5}x=

5

3−

5

if we solve it we get

5x - 3 + \sqrt{5} = 0.....eq(2)5x−3+

5

=0.....eq(2)

multiplying equation (1) and (2)

(5x - 3 - \sqrt{5} )(5x - 3 + \sqrt{5} ) = 0(5x−3−

5

)(5x−3+

5

)=0

using identities

(a + b) { }^{2} = a {}^{2} + b {}^{2} - 2ab(a+b)

2

=a

2

+b

2

−2ab

(a + b)(a - b) = {a}^{2} - b {}^{2}(a+b)(a−b)=a

2

−b

2

(5x - 3) {}^{2} - ( \sqrt{5} ) {}^{2}(5x−3)

2

−(

5

)

2

25x {}^{2} + 9 - 30x - 5 = 025x

2

+9−30x−5=0

25x {}^{2} - 30x + 4 = 025x

2

−30x+4=0