if alpha and beta are the zeros of the polynomial f(x)=x^2+3x+5, then alpha + beta by alpha beta
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Let alpha= a and beta=b. So the equation is x^2–3x-5. The product of its roots is a*b= —5 and sum of roots is a+b = 3. Now (a^2 + b^2)^2 = a^4 + b^ 4 + 2*a^2 * b^2.
Therefore a^4 + b^ 4=(a^2 + b^2)^2 —2*(a*b)^2.
Now a^2+b^2 = (a+b)^2 —2*a*b.
Plugging in the values of sum and product we get a^4 + b^ 4 as 311 and this is the answer.
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if alpha and beta are the zeros of the polynomial f(x)=x^2+3x+5
So,
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