Which of the following equations has the sum of its roots as 3? `x^2+3x-5=0` (b) `-x^2+3x+3=0` `sqrt(2)x^2-3/(sqrt(2))x-1=0` (d) `3x^2-3x-3=0`

Options

A. `2x^(2)-3x+6=0`
B. `-x^(2)+3x-3=0`
C. `sqrt(2)x^(2)-3/(sqrt(2))x+1=0`
D. `3x^(2)-3x+3=0`

Explanation

(a) Given that `2x^(2)-3x+6=0`
on comparing with `ax^(2)+bx+c=0` we get
`a=2,b=-3` and `c=6`
`:.` Sum of the roots `=(-b)/a=(-(-3))/2=3/2`
So sum of the roots of the quadratic equation `2x^(2)-3x+6=0` is not 3 so it is not the answer.
(b) Given that `-x^(2)+3x-3=0`
On compare with `ax^(2)+bx+c=0` we get
`a=-1,b=3` and `c=-3`
`:.` Sum of the roots `=(-b)/a=(-(3))/(-1)=3`
So, sum of the roots of the quadratic equation `-x^(2)+3x-3=0` is 3 so it is the answer
(c) Given that `sqrt(2)x^(2)-3/(sqrt(2))x+1=0`
`implies 2x^(2)-3x+sqrt(2)=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=2,b=-3` and `c=sqrt(2)`
`:.` sum of the roots `=(-b)/a=(-(-3))/2=3/2`
So sum of the roots of the quadratic equation `sqrt(2)x^(2)-3/(sqrt(2))x+1=0` is not 3, so it is not the answer.
(d) Given that `3x^(2)-3x+3=0`
`implies x^(2)-x+1=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=1, b=-1` and `c=1`
`:.` Sum of the roots `=(-b)/a=(-(-1))/1=1`
So, sum of the roots of the quadratic equation `3x^(2)-3x+3=0` is not 3, so it is not the answer.