MathematicsIf one zero of the polynomial 2×2-3x+k is reciprocal to the other, then find the value of k ?

If one zero of the polynomial $2 x^{2} - 3 x + k$ is reciprocal to the other, then find the value of $k$ ?

It is given that one zero of the polynomial

2 x^{2} - 3 x + k

is reciprocal of the other. We know that for the polynomial in the form a

x^{2}

+ bx + c = 0 , the product of its zeros is given by

\frac{c}{a}

. The product of zeros of the given polynomial will be

\frac{k}{2}

.
Since, one zero of the given polynomials is reciprocal of the other. So, their product will be equal to 1.

\Rightarrow \frac{k}{2} = 1

\Rightarrow k = 2

Therefore, k = 2.
Hence, the required option is 1.

JEE