Question

Please help… Will mark brainliest!!!

Answer 1

Answer:

value of a is -19

value of b is 10

Step-by-step explanation:

Given

p(x) = 6x³ + ax² + 9x + b

Since it is given (x-2) & (2x-1) are the factors of given polynomial p(x) .

So, x = 2 & x = -1/2 are the solutions of given polynomial .

when x = 2

p(2) = 6(2)³ + a(2)² + 9 (2) + b = 0

p(2) = 6×8 + 4a + 18 + b = 0

p(2) = 48 + 4a + 18 + b = 0

p(2) = 66 + 4a + b = 0

4a + b = -66 -------(i)

Now ,

when x = -½

p(-½) = 6(-½)³ + a (-½)² + 9(-½) + b = 0

6 × (-⅛) + a/4 - 9/2 + b = 0

-3/4 + a/4 - 9/2 + b = 0

-3 + a -18+4b/4 = 0

-21 + a + 4b = 0

a + 4b = 21 -------(ii)

Now, multiplying the equation (ii) by 4 we get

4a + 16b = 84 -----(iii)

Substracting equation (i) from (iii) we obtain

15b = 150

b = 150/15

b = 10

Now, putting the value of b = 10 in equation (ii) we get

a + 40 = 21

a = 21-40

a = -19

So, the required value of a & b are 10 & -19 respectively .