If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p ( ½).

1.	If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p ( ½).
Answer» Given that, p() =x² – 4x + 3 According to the question, When x = 2, p(x) = p(2) p() =x² – 4x + 3 Substituting x = 2, p(2) = (2)² – 4(2) + 3 = 4 – 8 + 3 = – 4 + 3 = – 1 When x = – 1, p(x) = p(– 1) p() =x² – 4x + 3 Substituting x = – 1, p(– 1) = (– 1)² – 4(– 1) + 3 = 1 + 4 + 3 = 8 When x = ½ , p(x) = p(½) p() =x² – 4x + 3 Substituting x = ½, p(½) = (½)² – 4(½) + 3 = ¼ – 2 + 3 = ¼ + 1 = 5/4 Now, p(2)− p(−1) + p(½) = – 1 – 8 + (5/4) = – 9 + (5/4) = ( – 36 + 5)/4 = – 31/4

Answer»

Given that,

p() =x² – 4x + 3

According to the question,

When x = 2,

p(x) = p(2)

p() =x² – 4x + 3

Substituting x = 2,

p(2) = (2)² – 4(2) + 3

= 4 – 8 + 3

= – 4 + 3

= – 1

When x = – 1,

p(x) = p(– 1)

p() =x² – 4x + 3

Substituting x = – 1,

p(– 1) = (– 1)² – 4(– 1) + 3

= 1 + 4 + 3

= 8

When x = ½ ,

p(x) = p(½)

p() =x² – 4x + 3

Substituting x = ½,

p(½) = (½)² – 4(½) + 3

= ¼ – 2 + 3

= ¼ + 1

= 5/4

Now,

p(2)− p(−1) + p(½) = – 1 – 8 + (5/4)

= – 9 + (5/4)

= ( – 36 + 5)/4

= – 31/4

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