Question

One of the zero is 2+root5 and sum of zeros is 4. Form a quadratic equation from the given information

Answer 1

Hi ,

Let m , n are two roots of the quadratic

equation ,

m = 2 + √5 ,

m + n = 4

2 + √5 + n = 4

n = 4 - 2 - √5

n = 2 - √5 ,

Now ,

sum of the roots = m + n = 4

product of the roots = mn

= ( 2 + √5 ) ( 2 - √5 )

= 2² - ( √5 )²

= 4 - 5

= -1

Required quadratic equation ,

x² - ( m + n )x + mn = 0

x² - 4x - 1 = 0

I hope this helps you.

: )

Answer 2

Hiii friend,

Let Alpha = 2+✓5


Sum of zeros = (Alpha × Beta)

4 = 2+✓5 + Beta

Beta = 4-2-✓5 => 2-✓5


Product of Zeros = (Alpha × Beta) = (2+✓5)(2-✓5) = (2)² - (✓5)² = 4-5 = -1.


Therefore,

Required POLYNOMIAL = X²-(Alpha+Beta)X+Alpha × Beta

=> X²-(4)X+(-1)

=> X²-4X-1


HOPE IT WILL HELP YOU....... :-)