If the solutions of the equation $x^{2} + 3 x - 18 = 0$ are -6, 3, then find the roots of the equation $2 (x^{2} + 3 x - 18) = 0$ .

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Solution

The roots of a quadratic equation do not change when it is multiplied by a constant non-zero real number. (0.5 mark)

So when the equation $x^{2} + 3 x - 18 = 0$ is multiplied by 2, the roots still remain the same i.e. -6 and 3. (0.5 mark)

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x^{2} + 3 x - 18 = 0

2 (x^{2} + 3 x - 18) = 0

x^{2} + 3 x - 18 = 0

- 6, 3

2 (x^{2} + 3 x - 18) = 0

If the solutions of the equation $x^{2} + 3 x - 18 = 0$ are -6, 3 then the roots of the equation $2 (x^{2} + 3 x - 18) = 0$ are

x^{2} + 3 x - 18 = 0

2 (x^{2} + 3 x - 18) = 0

If the roots of the equation, $x^{2} + 3 x - 18 = 0$ are $- 6, 3$ then the roots of the equation $2 (x^{2} + 3 x - 18) = 0$ are

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