Question

If p(x) = x2 - 4x+3, then find the value of p(2) - P(-1)+ P(1/2)​

Answer 1

$p(x) = {x}^{2} - 4x + 3$

$p(2) = {2}^{2} - 4(2) + 3 \\ \: \: \: \: \: \: \: \: \: = 4 - 8 + 3 = - 1$

$p( - 1) = {( - 1)}^{2} - 4( - 1) + 3 \\ \: \: \: \: \: \: \: \: \: \: \: = 1 + 5 + 3 = 9$

$p( \frac{1}{2}) = {( \frac{1}{2} )}^{2} - 4( \frac{1}{2}) + 3 \\ \\ \: \: \: \: \: \: \: \: \: \: = \frac{1}{4} - 2 + 3 = \frac{1 - 8 + 12}{4} = \frac{5}{4}$

Now,

$p(2) - p( - 1) + p( \frac{1}{2}) \\ \\ - 1 - 9 + \frac{5}{4} \\ \\ \frac{ - 4 - 36 + 5}{4} \\ \\ \frac{ - 40 + 5}{4} = \frac{ - 35}{4}$

${ \text{ \huge{Answer :-}}}$

${ \boxed{ \boxed{ \red{p(2) - p( - 1) + p( \frac{1}{2}) = \frac{ - 35}{4} }}}}$