Question

If p and q are the zeroes of the polynomial f(x)=3x2+5x+7, then find the value of 1/p^2 + 1/q^2
please answer with step by step​

Answer 1

Answer:

From relations between coefficients and roots of quadratic

$p + q = \frac{ - b}{a} = \frac{ - 5}{3} \\ \\ pq = \frac{c}{a} = \frac{ 7}{3}$

Now

$\frac{1}{ {p}^{2} } + \frac{1}{ {q}^{2} } \\ \\ = \frac{ {p}^{2} + {q}^{2} }{ {p}^{2} {q}^{2} } \\ \\ = \frac{(p + q) {}^{2} - 2pq }{(pq) {}^{2} } \\ \\ = \frac{( \frac{ - 5}{3}) {}^{2} - 2( \frac{7}{3} ) }{ (\frac{7}{3}) {}^{2} } \\ \\ = \frac{25 - 14 \times 3}{49} \\ \\ = - \frac{17}{49}$

Answer 2

$\huge\star\underline\mathfrak\purple{Hello!!}$

Refer to the attachment above for your answer!!✔✔