Question 35

Given $$2x^2 + 19x + 45 = 0$$ and $$2y^2 + 11y + 12 = 0$$, then which of the following regarding the roots x, y is TRUE?

Solution

$$2x^2 + 19x + 45 = 0$$

$$\Rightarrow 2x^2 + 10x + 9x + 45 = 0$$

$$\Rightarrow 2x(x + 5) + 9(x + 5) = 0$$

$$\Rightarrow (2x + 9)(x + 5) = 0$$

$$\Rightarrow$$ x = -9/2 = -4.5 or x = -5

$$2y^2 + 11y + 12 = 0$$

$$\Rightarrow 2y^2 + 8y + 3y + 12 = 0$$

$$\Rightarrow 2y(y + 4) + 3(y + 4)= 0$$

$$\Rightarrow (y + 4)(2y + 3) = 0$$

$$\Rightarrow$$ y = -4 or y = -3/2 = -1.5

Hence, x < y.

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