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Given that $x^2 \cdot (3x + 5) = 1 : 2$ find the possible values of x. - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 1

Question 19

$Given-that--$x^2-\cdot-(3x-+-5)-=-1-:-2$---find-the-possible-values-of-x.-Edexcel-GCSE Maths-Question 19-2019-Paper 1.png$

Given that $x^2 \cdot (3x + 5) = 1 : 2$ find the possible values of x.

Worked Solution & Example Answer:Given that $x^2 \cdot (3x + 5) = 1 : 2$ find the possible values of x. - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 1

Step 1

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Answer

To solve for the possible values of x, we first rewrite the equation from the given ratio:

$x^2 \cdot (3x + 5) = 1 / 2$

Multiplying both sides by 2 gives:

$2x^2(3x + 5) = 1$

Step 2

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Answer

Expanding the left side, we have:

$6x^3 + 10x^2 = 1$

Rearranging the equation results in:

$6x^3 + 10x^2 - 1 = 0$

Step 3

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Answer

Next, we can use numerical methods or factoring if we recognize any possible roots. Trying values using the Rational Root Theorem may lead us to:

$x = -\frac{1}{3}, \: x = \frac{1}{2}$

After testing these values in the equation, we can confirm them as roots.

Step 4

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Answer

The possible values of x satisfying the equation are:

$x = -\frac{1}{3}, \: x = \frac{1}{2}$

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