Question

if x+1 is a factor of 2x cube + ax square + 2bx +1 then find the values of a and b given that 2a-3b = 4​

Answer 1

Answer:

a = 5

b= 2

Step-by-step explanation:

given that x+1 is a factor

then x+1 = 0

x= -1

the equation is 2x^3 + ax^2 + 2bx +1

substitute x = - 1 in the above equation

2 ( -1 )^3 + a ( -1 )^2 + 2b( - 1 ) +1 = 0

-2 + a - 2b +1=0

-1 + a - 2b = 0

a - 2b = 1

multiply by 2

2 ( a - 2b ) = 2 (1 )

2a - 4b = 2 ..............consider as equation 1

given that 2a - 3b = 4 ..........consider as equation 2

do equation 1 - 2

2a-4b=2

( - ) 2a-3b=4

we will get

-b = -2

b = 2

now substitue b value in anyone of the equation 1 or equation 2

i am substituting in equation 2

2a - 3(2) = 4

2a- 6 = 4

2a = 6+4

2a = 10

a = 10/2

a = 5

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