What are the roots of $2x^2 - 5x - 3 = 0$ ?

-3

and

\frac{1}{2}

Correct answerYour answer

3

and

-\frac{1}{2}

Correct answerYour answer

6

and

-1

Correct answerYour answer

3

and

\frac{1}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Product $a \times c = 2 \times (-3) = -6$ ; split the middle term as $-6x + x$ .
$2x^2 - 6x + x - 3 = 2x(x - 3) + 1(x - 3) = (2x + 1)(x - 3)$ .
So $x = 3$ or $x = -\frac{1}{2}$ .

Worth noting

6 and $-1$ are the roots of $x^2 - 5x - 6$ : they come from forgetting that the leading coefficient is 2. $-3$ and $\frac{1}{2}$ have both signs flipped.

Concept: Factorising a quadratic with leading coefficient other than 1
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsQuadratic equations

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Ten questions from Linear and Quadratic Equations, at your own pace.

What are the roots of 2x2−5x−3=02x^2 - 5x - 3 = 02x2−5x−3=0?

Explanation

What are the roots of $2x^2 - 5x - 3 = 0$ ?