Question

Please answer this the question is attached

Answer 1

$\large \star \: \sf \underline{ \underline{ \: given : }} \\ \\ \large \sf \: p(x) = 2 {x}^{2} + 7x - 4$

$\large \sf \: taking \: \: value \: \: for \: \: x : \\ \\ \large \tt : \implies \: x = 2 \\ \\ \large \tt \: p(2) = 2( {2)}^{2} + 7(2) - 4 \\ \\ \large \tt : \implies p(2) = 2(4) + 14 - 4 \\ \\ \large \tt : \implies p(2) = 8 + 10 \\ \\ \large \tt : \implies p(2) = 18 \not = 0\\ \\ \large \sf \therefore \: \: x = 2 \: \: is \: \: not \: \: a \: \: zero \: \: of \: \: p(x)$

$\large \sf \: taking \: \: value \: \: for \: \: x : \\ \\ \large \tt : \implies \: x = \frac{1}{2} \\ \\ \large \tt \: p \left( \frac{1}{2} \right) = 2 {\left( \frac{1}{2} \right)}^{2} + 7\left( \frac{1}{2} \right)- 4 \\ \\ \large \tt : \implies p \left( \frac{1}{2} \right)= 2 \left( \frac{1}{4} \right)+ \left( \frac{7}{2} \right) - 4 \\ \\ \large \tt : \implies p\left( \frac{1}{2} \right) = \cancel2 \left( \frac{1}{ \cancel4 \: \: 2} \right)+ \left( \frac{7}{2} \right) - 4 \\ \\ \large \tt : \implies p \left( \frac{1}{2} \right)=\left( \frac{1}{2} + \frac{7}{2} \right) - 4\\ \\ \large \sf : \implies \: p\left( \frac{1}{2} \right) = \frac{8}{2} - 4 \\ \\ \large \sf : \implies \: p\left( \frac{1}{2} \right) = \frac{8 - 8}{2} \\ \\ \large \sf : \implies \: p\left( \frac{1}{2} \right) = \frac{0}{2} \\ \\ \large \sf : \implies \: p\left( \frac{1}{2} \right) = 0 \\ \\ \large \sf \therefore \: \: x = \frac{1}{2} \: \: is \: \: a \: \: zero \: \: of \: \: p(x)$

$\large \sf \: taking \: \: value \: \: for \: \: x : \\ \\ \large \tt : \implies \: x = \frac{ - 1}{2} \\ \\ \large \tt \: p \left( \frac{ - 1}{2} \right) = 2 {\left( \frac{ - 1}{2} \right)}^{2} + 7\left( \frac{ - 1}{2} \right)- 4 \\ \\ \large \tt : \implies p \left( \frac{ - 1}{2} \right)= 2 \left( \frac{1}{4} \right)+ \left( \frac{ - 7}{2} \right) - 4 \\ \\ \large \tt : \implies p\left( \frac{ - 1}{2} \right) = \cancel2 \left( \frac{1}{ \cancel4 \: \: 2} \right)+ \left( \frac{ - 7}{2} \right) - 4 \\ \\ \large \tt : \implies p \left( \frac{ - 1}{2} \right)=\left( \frac{1}{2} - \frac{7}{2} \right) - 4\\ \\ \large \sf : \implies \: p\left( \frac{ - 1}{2} \right) = \frac{ - 6}{2} - 4 \\ \\ \large \sf : \implies \: p\left( \frac{ - 1}{2} \right) = \frac{ - 6 - 8}{2} \\ \\ \large \sf : \implies \: p\left( \frac{ - 1}{2} \right) = \frac{ - 14}{2} \\ \\ \large \sf : \implies \: p\left( \frac{ - 1}{2} \right) = \frac{ - \cancel{1 4} \: \: 7}{ \cancel2} \\ \\ \large \sf: \implies \: p\left( \frac{ - 1}{2} \right) = - 7 \\ \\ \large \sf \therefore \: \: x = \left( \frac{ - 1}{2} \right)\: \: is \: \: not \: \: a \: \: zero \: \: of \: \: p(x)$