Question

Find the value of a and b if P(1) = 1 and P(2) = 7 in the polynomial P(x)=2x 3 – ax 2 +7x – b.

Answer 1

Answer:

a = 5

b = 3

Step-by-step explanation:

P(x) = 2x³ - ax² + 7x - b

For P(1) = 1

substitute 1 as the value of x

P(1) = 2(1)³ - a(1)² + 7(1) - b = 1

= 2 - a + 7 - b = 1

a+b = 2+7-1

a+b = 8 .........eq1

For P(2) = 7

substitute 2 as the value of x

P(2) = 2(2)³ - a(2)² + 7(2) - b = 7

= 2(8) - a(4) + 7(2) - b = 7

16 - 4a + 14 - b = 7

4a + b = 16 + 14 - 7

4a + b = 23........eq2

eq1 and eq2

4a + b = 23 ...eq2 solve simultaneously

a + b = 8 ...eq1

-----------------

subtract eq1 from eq2

3a = 15

a = 15/3

a = 5

from eq1

a + b = 8

5 + b = 8

b= 8-5

b= 3

a=5 , b=3

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