Question

plz solve fast.....31st question fast​

Answer 1

If the zeros of the quadratic polynomial is reciprocal to other then the zeros are x and 1/x

Product of zeros = c /a

( x)( 1/x) = c / a

a = c

Thus the value of c is a

.

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Answer 2

Answer:

c = a

Note:

★ The possible values of variable for which the polynomial becomes zero are called its zeros.

★ A quadratic polynomial can have atmost two zeros.

★ If A and B are the zeros of the quadratic polynomial ax² + bx + c , then ;

Sum of zeros , (A+B) = -b/a

Product of zeros , (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is ;

ax² + bx + c .

Also,

It is given that , the zeros of the given quadratic polynomial are reciprocal of each other .

Thus ,

Let A and 1/A be the zeros of the given quadratic polynomial.

Now,

=> Sum of zeros = -b/a

=> A + 1/A = -b/a

Also,

=> Product of zeros = c/a

=> A•(1/A) = c/a

=> 1 = c/a

=> a = c

=> c = a

Hence ,

If the zeros are reciprocal of each other , then c = a .

Observation :

If the zeros of a quadratic polynomial are reciprocal of each other , then the leading coefficient is equal to the constant .

( Leading coefficient : Coefficient of the term with highest degree of variable. )