Question

If one zero of polynomial 2x^2-3x+p is 3 then find the other root(zero).Also find the value of p​

Answer 1

Answer:

The other zero of the given polynomial is -3/2.

Step-by-step explanation:

Here, the given polynomial is,

2x^2-3x+p2x

2

−3x+p

Let, f(x) = 2x^2-3x+pf(x)=2x

2

−3x+p

Given,

3 is a zero of f(x),

⇒ f(3) = 0

\implies 2(3)^2-3(3)+p=0⟹2(3)

2

−3(3)+p=0

\implies 18-9+p = 0\implies p = -9⟹18−9+p=0⟹p=−9

Thus, the polynomial will be,

f(x) = 2x^2-3x-9f(x)=2x

2

−3x−9

=2x^2-6x+3x-9=2x(x-3)+3(x-3)=(2x+3)(x-3)=2x

2

−6x+3x−9=2x(x−3)+3(x−3)=(2x+3)(x−3)

When f(x) = 0

(2x+3)(x-3) = 0 ⇒ 2x+3 = 0 ⇒ x =-3/2

Thus, the other zero of the given polynomial is -3/2.