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In the polynomial p(x) = 2x2 + ax2 – 7x + b, p(1) = 3 and p(2) = 19. Find a and b.

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p(x) = 2x2 + ax2 – 7x + b

p(l) = 2 x 13 + a x 12 – 7 x 1 + b

= 2 + a – 7 + b = a + b + 2 – 7 = a + b – 5

p(1) = 3, a + b – 5 = 3

a + b = 8……… (1)

p(2) = 2 x 23 + a x 22 – 7 x 2 + b

= 16 + 4a – 14 + b = 4a + b + 2

p(x) = 19

4a + b + 2 = 19

4a + b = 17 ……….. (2)

(2) – (1)

3a = 9, a = 3 a + b – 5 = 3

From equation (1),

a + b = 8 

3 + b = 8 

b = 5

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