## If the zeroes of the polynomial 3×2 –11x+k are reciprocal to each other, then the value of k is [ ]​

Question

If the zeroes of the polynomial 3×2 –11x+k are reciprocal to each
other, then the value of k is
[ ]​

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1 month 2021-09-14T23:10:23+00:00 2 Answers 0 views 0

1. ### EXPLANATION.

• GIVEN

zeroes of the polynomial = 3x² – 11x + k

are reciprocal to each other.

### according to the question,

products of zeroes of quadratic polynomial

=> ab = c/a

quadratic polynomial are reciprocal to each

other => a X 1/a = 1

=> 1 = c/a

=> 1 = k/3

=> k = 3

### Value of k = 3

=> sum of zeroes of quadratic polynomial.

=> a + b = -b/a

=> products of zeroes of quadratic polynomial.

=> ab = c/a

### => x² – ( a + b )x + ab

Let one root of the given that other zero is Reciprocal the one zero.

So,

Other zero=1/Alpa.

Given polynomial is 5x

2

+13x+k=0.

Here,

A=coefficient of x

2

B=coefficient of x

And,C=constant term.

Product of zeroes =C/A

Alpha ×1/Alpha =K/5

1=K/5

K=5

Then,

We get k=5.