Question

If 3+√5 is a root of ax2 + cx + b = 0 and 4+√2 is a root of x2 – dx + e = 0, where a, b, c, d and e are rational numbers, then the value of b+c/ade is

Answer 1

Answer:

-6

Step-by-step explanation:

I hope it will help you

Answer 2

Answer:

The required value for b+c/ade is 10/112

Step-by-step explanation:

Given,

3+√5 is a root of ax2 + cx + b = 0

4+√2 is a root of x2 – dx + e = 0

Given equation is

a {x}^{2} + cx + b = 0 - - - - - 1

sum of roots for equation 1=

$3 + \sqrt{5} + 3 - \sqrt{5} = 6$

#

product of roots for equation 1=

$(3 + \sqrt{5)} (3 - \sqrt{5} )$

$= 4$

so the required equation is

$a {x}^{2} - (sum \: of \: roots) x\\ + product of \: roots\:$

$a {x}^{2} - 6x + 4$

comparing with above equation

c=-6

b=4

given equation 2 is

${x}^{2} - dx + e$

$|4 + - \sqrt{2} |$are the roots of the equation

sum of the roots=8

product of roots= 14

now equation formed

$a {x}^{2} - ( sum \: of \: roots)x + product \: of \: roots$

Here formed equation is

$a {x}^{2} - 8x + 14$

comparing with equation 2

a=1

d=8

e=14

Required values are b=4 c=6

a=1 d=8 e =14

we have to find value of

$\frac{b + c}{ade} = \frac{4 - 6}{14 \times 8}$

$\frac{ - 2}{112}$

so the required value for b+c/ade is -2/112

#SPJ1

kalyani