Question

If α and 1/α are the zeroes of the polynomial ax² + bx + c, then value of c is

Answer 1

products of zeroes = c/a

product s of zeroes = α × 1/α = 1

hence c/a = 1

c/a = 1

c = a

Answer 2

SOLUTION

GIVEN

α and 1/α are the zeroes of the polynomial ax² + bx + c

TO DETERMINE

The value of c

CONCEPT TO BE IMPLEMENTED

If $\sf \alpha \: \: and \: \: \beta \:$ are the zeroes of the quadratic polynomial ax² + bx + c

Then

$\displaystyle \sf \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

EVALUATION

Here the given polynomial is ax² + bx + c

Now it is given that α and 1/α are the zeroes of the polynomial ax² + bx + c

$\displaystyle \sf \: Sum \: of \: the \: zeroes = - \frac{b}{a}$

$\displaystyle \sf Product \: of \: the \: zeroes = \frac{c}{a}$

$\displaystyle \sf \implies \: \alpha \times \frac{1}{ \alpha } = \frac{c}{a}$

$\displaystyle \sf \implies \: 1 = \frac{c}{a}$

$\displaystyle \sf \implies \: \frac{c}{a} = 1$

$\displaystyle \sf \implies \: c = a$

FINAL ANSWER

Hence the required value of c = a

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