Question

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is
(a) x² + 4= 0
(b)x²− 4= 0
(c)4x² − 1= 0
(d)x ²− 2= 0

Answer 1

SOLUTION :  

Option (b) is correct : x² - 4 = 0

Let α be the one root  of the equation and β be the other root .

Given : α = 2, α + β = 0

α + β = 0

2 + β = 0

β = - 2

The value of α = 2 and  β = - 2 ………(1)

Product of zeroes = α × β  

α × β = 2 ×  - 2  

α β = - 4……………(2)

if α  and β are the zeros of the quadratic equation, then quadratic equation will be :  

[x² - (α +  β)x + α β]

[x² -(2 -2)x + (-4)]

[From eq 1 & 2 ]

x² - 0 × x - 4  

x² - 4 = 0

Hence, the quadratic equation is x² - 4 = 0

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

${x}^{2} - 4 \: \: \: is \: answer$