Question

If a quadratic equation whose one root is 1+root 2 and the sum of its roots is 2 is

Answer 1

here we have to find the quadratic equation whose one root is 1+ √2 and the sum of its roots is 2.

let the other root of the equation be x.

➡ 1 + √2 + x = 2

➡ x = 2 - 1 - √2

➡ x = 1 - √2

another root of the quadratic equation is 1 - √2

therefore product of the roots = (1 + √2)(1 - √2)

using identity (a + b)(a - b) = a² - b²

= (1)² - (√2)²

= 1 - 2

= -1

now we know that,

sum of roots = -b/a

product of roots = c/a

• 2 = -b/a

➡ b/a = -2

• -1 = c/a

therefore a = 1, b = -2 and c = -1

standard form of quadratic equation = ax² + bx + c

hence, the quadratic equation is =

x² - 2x - c

Answer 2

$\mathsf{\huge{\underline{\boxed{Equation:x^2-2x-c}}}}$

$\rule{200}{2}$

$\mathfrak{\large{\underline{\underline{Explanation}}}}$

First root :- 1+√2

let other root be x

So,

» x+1+√2 = 2

» x = 2-1-√2

» x = 1- √2

☞ So, other root is 1-√2

__________________________

Product of roots :-

» (1+√2)(1-√2)

» (1)² - (√2)² [ By a² - b² = (a+b)(a-b)]

» 1-2

» -1

$\rule{200}{1}$

We know :-

sum of roots = -b/a

products of roots = c/a

$\rule{200}{1}$

» 2 = -b/a

» b/a = -2

» c/a = -1

a=1, b= -2 , c= -1

_________________________

So, general form of equation is

ax² + bx + c

______________

A.T.Q,

x² - 2x - c