Which of he following equations has the sum of its roots as 3?   (A) x^2 + 3x - 5 = 0 (B) -x^2 + 3x +3 =0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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For the given equations:

For a quadratic equation ax^2 + bx + c = 0, the roots are [-b+ sqrt (b^2 - 4ac)]/2a and  [-b - sqrt (b^2 - 4ac)]/2a. The sum of the two roots is -2b / 2a = -b/a

We have the equations : x^2 + 3x - 5 = 0 and -x^2 + 3x +3 =0

The sum of the roots of x^2 + 3x - 5 = 0 is -b /a = -3

The sum of the roots of -x^2 + 3x +3 =0 is -b/a = 3

Therefore the equation -x^2 + 3x +3 =0 has the sum of its roots as 3.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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We know that if ax^2 + bx + c = 0 is a quadratic equation, x1 and x2 are the roots, Then:

1. x1 + x1 = -b/a

2. x1*x2= c/a

Let us use the rule to determine the roots for both equations.

For the equation x^2 + 3x -5 = 0

==> x1+ x2 = -b/a = -3/1 = -3

For the equation -x^2 + 3x+3 = 0

==> x1+x2 = -b/a = -3/-1 = 3

Then the equation with the sum of its roots = 3 is (-x^2 +3x +3 = 0)

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