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# algebra

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The roots of x^2 + x - 3 = 0 are p and q. Calculate 4p^2 - q^3.

Jan 26, 2022

#1
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We have a quadratic, and since the first step is to find the roots, we can apply the quadratic formula: $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$, where $$a$$ is the coefficient of $$x^2$$$$b$$ is the coefficient of $$x$$, and $$c$$ is the constant.

Now to plug in the values.

$$x = {-1{+\over}\sqrt{13}\over2}$$

The plus operation and the minus operation are the roots p and q, respectively.

Now I used a calculator, and $$4p^2$$ approximates to 6.7889.

$$q^3$$ approximates to -12.2111.

Since we are subtracting $$q^3$$ from $$4p^2$$, that is 6.7889 - (-12.2111) = 19

Thus, $$4p^2 - q^3 = 19$$.

Jan 26, 2022