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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, \(4p^2 - q^3 = 19\).

 

smiley

 Jan 26, 2022

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