Solve for x: 3x^2 - 7x + 2 = 0. | Mathematics MCQ | Examoogle

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Solve for x: 3x² - 7x + 2 = 0.

$2, 1/3$

$1, 2/3$

$2, -1/3$

$3, 1/2$

Correct Answer

📐 MA • Math Splitting Middle TermMathematicsMathematics

Option A

$2, 1/3$

Quick Summary:

Use the product and sum rule: find two numbers that multiply to $a imes c = 6$ and add to $b = -7$ . These are $-6$ and $-1$ . Divide these by the leading coefficient $3$ and change the sign to get the roots: $6/3 = 2$ and $1/3$ .

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📐MAMath SolutionSplitting Middle Term

📋 Given

A quadratic equation $3x^2 - 7x + 2 = 0$ is provided where coefficients are $a=3, b=-7, c=2$ .

🔢 Formula Used

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac​​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

A frequent mistake is to neglect the negative sign on $b$ when substituting into the quadratic formula or failing to divide by $2a$ at the end of the splitting method.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify coefficients

From the quadratic equation $3x^2 - 7x + 2 = 0$ , identify the coefficients $a=3$ , $b=-7$ , and $c=2$ .

a=3,b=−7,c=2a=3, b=-7, c=2a=3,b=−7,c=2

Apply Middle Term Splitting

Split the middle term $-7x$ into $-6x$ and $-1x$ such that their product is $3 imes 2 = 6$ .

3x2−6x−x+2=03x^2 - 6x - x + 2 = 03x2−6x−x+2=0

Factorize by grouping

Group the terms and factor out common components: $3x(x - 2) - 1(x - 2) = 0$ , which simplifies to $(3x - 1)(x - 2) = 0$ .

(3x−1)(x−2)=0(3x - 1)(x - 2) = 0(3x−1)(x−2)=0

Solve for x

Set each factor to zero to find the roots: $3x - 1 = 0 \implies x = 1/3$ and $x - 2 = 0 \implies x = 2$ .

x=2,x=13x = 2, x = \frac{1}{3}x=2,x=31​

✅

A is correct because the factors of the equation yield the roots $x = 2$ and $x = 1/3$ .

Core Concepts Used

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Quadratic Equations Factorization Method Roots of Polynomials

💡 EXAM TIP

This method of finding roots is the foundation for solving higher-degree polynomials and finding the vertex of a parabola in coordinate geometry.

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