Question

form the polynomial equation with rational coefficients whose roots are i-√5​

Answer 1

SOLUTION

TO DETERMINE

Form the polynomial equation with rational coefficients whose roots are i - √5

EVALUATION

Here we have to find the polynomial equation with rational coefficients whose roots are i - √5

$\sf{x = i - \sqrt{5} }$

$\sf{ \implies \: x + \sqrt{5} = i }$

Squaring both sides we get

$\sf{ \: {(x + \sqrt{5} )}^{2} = {i}^{2} }$

$\sf{ \implies \: {x}^{2} + 2x \sqrt{5} + 5 = - 1}$

$\sf{ \implies \: {x}^{2} + 6 = - 2x \sqrt{5} }$

Squaring both sides we get

$\sf{ \: {({x}^{2} + 6 )}^{2} = {(- 2x \sqrt{5} )}^{2} }$

$\sf{ \implies \: {x}^{4} + 12 {x}^{2} + 36 = 20 {x}^{2} }$

$\sf{ \implies \: {x}^{4} + 12 {x}^{2} + 36 - 20 {x}^{2} = 0 }$

$\sf{ \implies \: {x}^{4} - 8 {x}^{2} + 36 = 0 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If 1/2 is a root of the quadratic equation x²-mx-5/4=0 , then the value of m is?

https://brainly.in/question/21062028

2.Find the roots of the quadratic equation 6x2 +5x + 1 =0 by method of completing the squares.

https://brainly.in/question/30446963

3. Write a quadratic equation whose root are -4 and -5

https://brainly.in/question/24154410