Determine whether the given values of x are zeroes of the given polynomialor not: (3x+8)(2x+5); x = , x =

Let p(x) = (3x+8)(2x+5)

x = = 8/3 and x = = 5/2

So, if x = 8/3 is a zero of the polynomial p(x), then it must satisfy p(8/3) = 0.

So, on putting x = 8/3 in the above equation, we get:

p(8/3) = (3 × (8/3) + 8)(2 × (8/3) + 5)

= (8 + 8)(16/3 + 5)

= 16 × (31/3)

= 496/3 ¹ 0.

Therefore the given value of x is not a zero of the given polynomial.

If x = 5/2 is a zero of the polynomial p(x), then it must satisfy p(5/2) = 0.

So, on putting x = 5/2 in the above equation, we get:

p(5/2) = (3 × (5/2) + 8)(2 × (5/2) + 5)

= (15/2 + 8)(5 + 5)

= (31/2) × (10)

= 310/2

= 155 ¹ 0.

Therefore the given value of x is not a zero of the given polynomial.