Question

if P and Q are the zeroes of the polynomial ax2+bx+c find the values of p2 +q2

Answer 1

this is ur solution...

Answer 2

$Given \: p \: and \: q \: are \: the \: zeroes$

$of \: the \: polynomial \:ax^{2}+bx+c$

$i) Sum \:of \: zeroes = \frac{- x \: Coefficient }{x^{2} \: Coefficient }$

$\implies p+q = \frac{-b}{a} \: --(1)$

$ii) Product \:of \: zeroes = \frac{Constant \:term }{x^{2} \: Coefficient }$

$\implies pq = \frac{c}{a} \: --(2)$

$Now, \red{ Value \: of \: p^{2} + q^{2}}$

$= ( p + q )^{2} - 2pq$

$= \Big( \frac{-b}{a}\Big)^{2} - 2 \times \frac{c}{a}$

$= \frac{ b^{2} - 2ac}{a^{2}}$

Therefore.,

$\red{ Value \: of \: p^{2} + q^{2}}$

$\green { = \frac{ b^{2} - 2ac}{a^{2}}}$

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