Question

If two roots of a quadratic equation are √2 and 1 then form the quadratic equation.

Answer 1

Let α and β are the roots of a quadratic equation.

Given: (α)= √2 ,  β= 1
Sum of zeroes (α+ β)= (√2+1)
(α+ β)= (√2+1)

Product of zeroes (α. β) = √2 × 1= √2
α. β = √2

Required quadratic equation= k [x²-(Sum of zeroes)x +( Product of zeroes)]
= k[ x² -(α+ β)x +(α. β], where k is a non zero real number.

= x² -(√2+1)x + √2   [ here k = 1]

Hence, a quadratic equation is  = x² -(√2+1)x + √2.

HOPE THIS WILL HELP YOU...

Answer 2

HEYA MATE!!

GIVEN,

ZEROS==>
$\sqrt{2}$
,1.

LET THE ZEROS BE α,β.

α+β==>(√2+1) ...(I)
α.β==>(√2*1)==>(√2) ....(II)

QUADRATIC EQUATION ==>
x²-(α+β)x+(α.β)
==>x²-(√2+1)+√2[ANSWER]

HOPE IT HELPS YOU ☺☺☺