Question

Show that 2 and -1/3 are the zeros of polynomial p (x) = 3x^2-5x-2.

Answer 1

your answer is here
hope you understand

Answer 2

Answer:

Given:

p(x) = 3x² -5x-2

and zeros 2 and -1/3

To prove : they are the zeros

     we know that ,if 'a' is a zero of polynomial p(x) then p(a)=0.Thus, we have to substitute the given numbers in place of x

first ,take x= 2

p(x) = 3x²-5x-2

⇒ p(2) = 3(2²)-5*2-2

          = 3*4-10-2

          = 12-12

         = 0

Hence, 2 is a root (zero) of the given polynomial.

second case , take x = -1/3

p(x)=3x²-5x-2

$p(\dfrac{-1}{3}) = 3*(\dfrac{-1}{3})^2 -5*\dfrac{-1}{3}-2\\= 3*\dfrac{1}{9} +\dfrac{5}{3}-2\\\\=\dfrac{1}{3}+\dfrac{5-6}{3} [taking\:L.C.M]\\\\\implies \dfrac{1+5-6}{3}=\dfrac{6-6}{3}=\dfrac{0}{3}=0$

Hence, -1/3 is another zero of the polynomial