Question

. Let R1 and R2 are the remainder when the polynomial x3+2x2-5ax+7 and x3+9x2-12x +6 are divided by (x+1) and (x-2). If 2R1+R2=6, find the value of a. plz help me to get answer its very urgent plz

Answer 1

R1=-1+2+5a+7
R1=5a+8

R2=8+36-24+6
R2=26

2*(5a+8)+26=6
10a+16+26=6
a=-36/10
=-3.6

Answer 2

Answer:

Value of a is -3.6.

Step-by-step explanation:

Given polynomials,

x³ + 2x² - 5ax + 7      and  x³ + 9x² - 12x + 6

R1 and R2 is remainder when polynomials divided by  x + 1  and x - 2

2 × R1 + R2 = 6

To find: Value of a.

Let, p(x) = x³ + 2x² - 5ax + 7

q(x) = x³ + 9x² - 12x + 6

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 ) = (-1)³ + 2(-1)² - 5a(-1) + 7 = -1 + 2 + 5a + 7 = 5a + 8

R2 = q( 2 ) = (2)³ + 9(2)² - 12(2) + 6 = 8 + 36 - 24 + 6 = 26

Now,

2 × R1 + R2 = 6

2( 5a + 8 ) + 26 = 6

10a + 16 = -20

10a = -36

a = -3.6

Therefore, Value of a is -3.6.