Question

If 2 is a zero of both the polynomial 3x²+ax-14 and 2x³+bx²+x-2, then value of a-2b is ​

Answer 1

=2

3x²+ax-14

putting value of x that is 2 we get the value of a because being zero it give 0 after solving.

3×(2)²+a×2-14=0

3×4+2a-14=0

12-14=-2a

-2=-2a

1=a

now putting value of x in second equation,

2x³+bx²+x-2=0

2×(2)³+b×(2)²+2-2=0

2×8+4b=0

16+4b=0

4b=-16

b=-4

putting value of a & b in third equation,

2a+3b

=2×1+3×(-4)

=2-12

=-10

Answer 2

Answer :

Since 2 is a zero of both the polynomial

Put x = 2 in both polynomial and equate to 0

3x²+ax-14

3*4 + 2a -14 = 0

2a = 2

a = 1

2x³+bx²+x-2

2*8 + 4b = 0

4b = -16

b= -4

a-2b = 1 - 2*-4 = 9