Question

If P(x) is a quadratic polynomial with P(0) = 6, P(1) = 1 and P(2) = 0, then the value of P(3) is ...​

Answer 1

Given : P(x) is a quadratic polynomial with P(0) = 6, P(1) = 1 and P(2) = 0,

To Find : value of P(3)  

Solution

P(x) is a quadratic polynomial

P(x)  = ax² + bx + c

P(0) = 6,

=> a(0)² + b(0) + c = 6

=>  c= 6

P(x)  = ax² + bx + 6

P(1) = 1,

=> a(1)² + b(1) + 6 = 1

=>  a + b = - 5

P(2) = 0,

=> a(2)² + b(2) + 6 = 0

=>  4a + 2b = - 6

=> 2a + b = - 3

2a + b = - 3

a + b = - 5

=> a  = 2

    b = - 7

P(x)  = 2x² -7x + 6

P(3) = 2(3)² - 7(3) + 6

= 18 - 21 + 6

= 3

P(3) = 3

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