Given : P(x) is a quadratic polynomial with P(0) = 4, P(1) = 10 and P(-1) = 2,

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To Find : value of P(3)  

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Solution

P(x) is a quadratic polynomial

P(x)  = ax² + bx + c

P(0) = 4,

=> a(0)² + b(0) + c = 4

=>  c= 4

--

P(x)  = ax² + bx + 4

P(1) = 10,

=> a(1)² + b(1) + 4 = 10

=>  a + b = 6

--

P(-1) = 2,

=> a(-1)² + b(-1) + 4 = 2

=>  a + (-b) = - 2

=> a - b = - 2

--

a - b = - 2  

a + b = - 6  (-)

-2b   = 4

b       = -2

---

a + b = -6

a + (-2) = -6

a = -4

=> a  = -4

   b = --2

P(x)  = -4x² -2x + 4

P(3) = -4(3)² - 2(3) + 4

= -36 - 6 + 4

= -38

P(3) = -38

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by Sinogen