Question

If one zero of 3x² – 8x + k be the reciprocal of the other, then k = ? 

(a) 3 

(b) -3

(c) \(\frac{1}3\) 

(d) \(\frac{-1}3\)

Answer 1

Correct option is (a) 3

One zero of the polynomial 3x² + 8x + K is reciprocal of the other.

Assume that, “one of the zero of the above polynomial” is x, then another zero will be taken as \(\frac 1x\)

The product of the zeroes will be,

\((x) (\frac 1x) = \frac{\text{constant}}{x^2\text{coefficient }}\)

\(1 = \frac K3\)

\(K = 1 \times 3\)

\(K = 3\)

Thus, the value of K will be 3.

Answer 2

(a) k = 3 

Let α and \(\frac{1}α\) be the zeroes of 3x² – 8x + k. 

Then the product of zeroes = \(\frac{k}3\)

⇒ α × \(\frac{1}α\) = \(\frac{k}3\)

⇒ 1 = \(\frac{k}3\)

⇒ k = 3