Question

if X + 2 and x minus 3 are factors of 2 x cube + a x square + bx - 18 find the values of a and b​

Answer 1

Answer:

a=-13 and b = 27

Step-by-step explanation:

x-2 =0 and x-3 =0

therefore, x =2 and x = 3 must satisfy this equation

$2 {x}^{3} + a {x}^{2} + bx - 18$

$2( {2}^{3} ) + a {2}^{2} + b2 - 18 = 0$

16+4a+2b-18=0

4a+2b-2=0

2a+b-1=0 --------> equation 1

similarly for x=3

$2 {x}^{3} + a {x}^{2} + bx - 18$

$2( {3}^{3} ) + a {3}^{2} + b3 - 18 = 0$

54+9a+3b-18=0

9a+3b+36=0

3a+b+12=0 ----------> equation 2

subtracting equation 1 from equation 2

a+13=0

a=-13

putting the value of a =-13 in equation 1

-26+b-1=0

b=27