Question

If zeros of the polynomial 5x2-7x+k are the reciprocal of each other, then find the value of k

Answer 1

one zero is reciprocal to other.

product of zeros is 1

Therefore k/5=1

k=5

Answer 2

The value of k is 5.

Step-by-step explanation:

Consider the provided expression.

$5x^2-7x+k$

If the equation is in the form of $ax^2+bx+c=0$ then the product of its roots α and β is: $\alpha \beta =\dfrac{c}{a}$

Compare the provided equation with $ax^2+bx+c=0$

The value of a=5, b=-7 and c=k

It is given that the roots are reciprocal to each other.

So one root is k and another is 1/k.

$k\times\dfrac{1}{k}=\dfrac{k}{5}$

$1=\dfrac{k}{5}$

$k=5$

Hence, the value of k is 5.

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