<s>[INST] If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$ 
If the roots of the equation $x^2 + 3x -1 = 0$ also satisfy the equation $x^4 + ax^2 + bx + c = 0$ find the value of $a + b + 4c + 100$

I tried really hard but the most I could get is the sum of the roots of the second equation is $3$
Please could someone solve this please !
It would mean the world to me
 [/INST] Hint: The solutions of your polynomial are given by
$$x_{1,2}=-\frac{3}{2}\pm\frac{\sqrt{13}}{2}$$
plugging $x_1$ into the other equation we get
$$b\sqrt{13}+3c\sqrt{13}-3\sqrt{13}+2a+3b+11c+11=0$$
the rest is for you!
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