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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
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Solution
–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
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