Question

Which of the following equations has the sum of its roots 3 ?
1) 2x2-3x+9=0
2) -x2+3x-3=0
3) 3x2-3x+3=0

Answer 1

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Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

If a quadratic equation is defined as

$ax^2+bx+c=0$

Then the sum of its roots is $-\frac{b}{a}$.

In option 1:

The given equation is

$2x^2-3x+9=0$

The value of a is 2 and the value of b is -3.

$-\frac{b}{a}=-\frac{-3}{2}=\frac{3}{2}$

The sum of its roots is not equal to 3. Therefore option 1 is incorrect.

In option 2:

The given equation is

$-x^2+3x-3=0$

The value of a is -1 and the value of b is 3.

$-\frac{b}{a}=-\frac{3}{-1}=3$

The sum of its roots is 3. Therefore option 2 is correct.

In option 3:

The given equation is

$3x^2-3x+3=0$

The value of a is 3 and the value of b is -3.

$-\frac{b}{a}=-\frac{-3}{3}=1$

The sum of its roots is not equal to 3. Therefore option 3 is correct.