Question

write two quadratic equations whose roots are values log81 to base 2 log100to base10​

Answer 1

The required quadratic equation is x^2-4x-1=0x

2

−4x−1=0

Step-by-step explanation:

Given : One root of quadratic equation is 2+\sqrt{5}2+

5

To find : The quadratic equation

Solution :

we know, if 2+\sqrt{5}2+

5

is one of the root of quadratic equation then,

x=2+\sqrt{5}x=2+

5

x-2=\sqrt{5}x−2=

5

Squaring both side,

(x-2)^2=(\sqrt{5})^2(x−2)

2

=(

5

)

2

x^2+4-4x=5x

2

+4−4x=5

x^2+4-4x-5=0x

2

+4−4x−5=0

x^2-4x-1=0x

2

−4x−1=0

Therefore, The required quadratic equation is x^2-4x-1=0x

2

−4x−1=0 .