Question

Which of the following equations has the sum of its roots as 3?

Options

• 2x² – 3x + 6 = 0

• –x² + 3x – 3 = 0

• `sqrt(2)x^2 - 3/sqrt(2)x + 1` = 0

• 3x² – 3x + 3 = 0

Answer 1

–x² + 3x – 3 = 0

Explanation:

The sum of the roots of a quadratic equation ax² + bx + c = 0, a ≠ 0 is given by,

Coefficient of x / coefficient of x² = `-(b/a)` 

(A) Given, 2x² – 3x + 6 = 0

Sum of the roots = `(-b)/a`

= `(-(-3))/2`

= `3/2`

(B) Given, –x² + 3x – 3 = 0

Sum of the roots = `(-b)/a`

= `(-(3))/(-1)`

= 3

(C) Given, `sqrt(2)x^2 - 3/sqrt(2)x + 1` = 0

`2x^2 - 3x + sqrt(2)` = 0

Sum of the roots = `(-b)/a`

= `(-(-3))/2`

= `3/2`

(D) Given, 3x² – 3x + 3 = 0

Sum of the roots = `(-b)/a`

= `(-(-3))/3`

= 1