Question

if alpha and beta are the zeros of the polynomial f(x)=x^2+3x+5, then alpha + beta by alpha beta​

Answer 1

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.

Answer 2

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ANSWER}}}$

if alpha and beta are the zeros of the polynomial f(x)=x^2+3x+5

So,

$\alpha + \beta = - 3 \\ \alpha \beta = 5 \\ \\ now \\ \frac{ \alpha + \beta }{ \alpha \beta } \\ = \frac{ - 3}{5}$