Find the sum of the roots of the quadratic equation $ 3x^2 - 1... | Mathematics MCQ | Examoogle

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Find the sum of the roots of the quadratic equation $3x^2 - 12x + 9 = 0$ .

Correct Answer

📐 MA • Math Direct FormulaMathematicsAlgebra

Option B

Quick Summary:

For a quadratic equation $ax^2 + bx + c = 0$ , the sum of roots is simply the negation of the coefficient of $x$ divided by the coefficient of $x^2$ . Here, $-( -12 ) / 3 = 12 / 3 = 4$ .

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📐MAMath SolutionDirect Formula

📋 Given

A quadratic equation in the form of 3x² - 12x + 9 = 0.

🔢 Formula Used

Sum=−ba\text{Sum} = -\frac{b}{a}Sum=−ab​

⚡ Exam Hall Shortcut / Speed Trick

For a quadratic equation $ax^2 + bx + c = 0$ , the sum of roots is simply the negation of the coefficient of $x$ divided by the coefficient of $x^2$ . Here, $-( -12 ) / 3 = 12 / 3 = 4$ .

⚠️ Common Student Trap / Pitfall

Students often forget to include the negative sign of the coefficient $b$ when applying the formula $-b/a$ , leading to an incorrect result of $-4$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify coefficients

Compare the given equation $3x^2 - 12x + 9 = 0$ with the standard form $ax^2 + bx + c = 0$ to find the values of $a$ , $b$ , and $c$ .

a=3,b=−12,c=9a = 3, b = -12, c = 9a=3,b=−12,c=9

Apply the sum of roots formula

The sum of the roots for a quadratic equation is given by the formula $-\frac{b}{a}$ .

Sum=−ba\text{Sum} = -\frac{b}{a}Sum=−ab​

Substitute and calculate

Substitute the values of $a$ and $b$ into the formula to calculate the final sum.

Sum=−−123=123=4\text{Sum} = -\frac{-12}{3} = \frac{12}{3} = 4Sum=−3−12​=312​=4

✅

B is correct because the sum of the roots calculated using the formula $-b/a$ equals 4.

Core Concepts Used

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Quadratic Equation Vieta's Formulas Polynomial Roots

💡 EXAM TIP

Understanding Vieta's formulas is crucial for competitive exams as it allows you to find the sum and product of roots without solving the quadratic equation fully, which is a major time-saver in Algebra and Coordinate Geometry.

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