let r(1) and.r(2) are the reminder when the. p(x) =4x3+3x2-12ax-5 and p(x) =2x3+9x2-6x+2. are divided by x-1 & x-2. respectively . if 3r (1) + r(2). + 28 =0. find the value of r.
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polynomials,
p(x) = 4x³ + 3x² - 12ax - 5
and g(x) = 2x³ + 9x² - 6x + 2
R1 and R2 is remainder when polynomials divided by x - 1 and x + 2
3 × R1 + R2 + 28 = 0
To find: Value of a.
Using Remainder theorem which states that if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).
According tot remainder theorem,
R1 = p( 1 ) = 4(1)³ + 3(1)² - 12a(1) - 5 = 4 + 3 - 12a - 5 = 2 - 12a
R2 = g( -2 ) = 2(-2)³ + 9(-2)² - 6(-2) + 2 = -16 + 9×4 + 12 + 2 = 36 - 2=34
and
3 × R1 +3× R2 + 28 = 0
3( 2 - 12a ) + 3×34 + 28 = 0
6 - 36a + 102 + 28 = 0
-36a = -124
a = 124/36
regarding ([email protected])
p(x) = 4x³ + 3x² - 12ax - 5
and g(x) = 2x³ + 9x² - 6x + 2
R1 and R2 is remainder when polynomials divided by x - 1 and x + 2
3 × R1 + R2 + 28 = 0
To find: Value of a.
Using Remainder theorem which states that if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).
According tot remainder theorem,
R1 = p( 1 ) = 4(1)³ + 3(1)² - 12a(1) - 5 = 4 + 3 - 12a - 5 = 2 - 12a
R2 = g( -2 ) = 2(-2)³ + 9(-2)² - 6(-2) + 2 = -16 + 9×4 + 12 + 2 = 36 - 2=34
and
3 × R1 +3× R2 + 28 = 0
3( 2 - 12a ) + 3×34 + 28 = 0
6 - 36a + 102 + 28 = 0
-36a = -124
a = 124/36
regarding ([email protected])
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