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Mathematics

The quadratic equation 2x2 - 9x + 12 = 0.

Statement (1): Sum of the roots of the equation = 4124\dfrac{1}{2}.

Statement (2): In an quadratic equation ax2 + bx + c = 0, sum of the roots = −ba-\dfrac{\text{b}}{\text{a}}.

Options

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Quadratic Equations

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Answer

Both the statements are true.

Reason

The given quadratic equation 2x2 - 9x + 12 = 0

Here, a = 2

b = -9

c = 12

Sum of roots = −ba=−−92=92=412-\dfrac{\text{b}}{\text{a}} = -\dfrac{-9}{2} = \dfrac{9}{2} = 4\dfrac{1}{2}

So, Statement (1) is true.

Statement (2) is a well-known property of quadratic equations. The sum of the roots of a quadratic equation ax2 + bx + c = 0 is indeed −ba-\dfrac{\text{b}}{\text{a}}

So, Statement (2) is true.

Hence, option 1 is correct.

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