To determine To find: The solution of the given equation nearest to the hundredth. Explanation Given: The given equation is 2 x 2 − 8 x + 3 = 0 [ 3 , 4 ] Calculation: Newton’s approximation method can be expressed as, C n + 1 = C n − f ( C n ) f ′ ( C n ) Here, C n is current approximation value and C n + 1 upcoming approximation value. Consider f ( x ) = 2 x 2 − 8 x + 3 (1) Now, differentiate the above expression with respect to x . f ′ ( x ) = 4 x − 8 (2) Substitute x = 3 in equation (1). f ( 3 ) = 2 ( 3 ) 2 − 8 ⋅ 3 + 3 = 18 − 24 + 3 = − 3 Substitute x = 4 in equation (1). f ( 4 ) = 2 ( 4 ) 2 − 8 ⋅ 4 + 3 = 32 − 32 + 3 = 3 Substitute x = 3 in equation (2). f ′ ( 3 ) = 4 ⋅ 3 − 8 = 4 Check the values ( f ( 3 ) < 0 ) and ( f ( 4 ) > 0 ) , the values of f ( 3 ) and f ( 4 ) are in opposite sign so there is a solution for the equation lie in interval ( 3 , 4 ) . Consider an initial value C 1 = 3 Substitute the value of f ( C 1 ) , f ′ ( C 1 ) , C 1 and n = 1 for first iteration in Newton’s formula. C 1 + 1 = C 1 − f ( C 1 ) f ′ ( C 1 ) C 2 = C 1 − f ( 3 ) f ′ ( 3 ) = 3 − ( − 3 ) 4 = 3

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Chapter 12.6, Problem 2E

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To find: The solution of the given equation nearest to the hundredth.

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Chapter 12.6, Problem 1E

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