Question

3. If zeroes of p(x) = 2x2 – 7x + k are reciprocal of each other, then value of k is __________.

Answer 1

given

2x^2 - 7x +k are reciprocal of each other

as we know that product of reciprocal = 1

a*1/a = 1

product of roots c/a = k/2

1 = k/2

=> k= 2

Answer 2

QUESTION:

If zeroes of p(x) = 2x2 – 7x + k are reciprocal of each other, then value of k is __________.

ANSWER:

Let,

one zero of the polynomial be

$\huge\blue { \alpha}$

then the other zero of the polynomial be

$\huge\orange {\frac{1}{ \alpha } }$

we use the formula of product of zeroes to find the value of k .

$product \: of \: zeroes = \frac{constant \: term}{coefficient \: of \: {x}^{2} } = \frac{c}{a}$

now come to main question;

Here;

c = k

a = 2

Using the formula;

$\alpha \times \frac{1}{ \alpha } = \frac{k}{2} \\ 1 = \frac{k}{2}$

$2 = k$

FINAL ANSWER:

$\huge\purple {k = 2}$

Additional information;

Quadraticpolynomial is in the form of

$a {x}^{2} + bx + c = 0$

where;

b = sum of zeroes

c = product of zeroes

2.

$sum \: of \: zeroes = \frac{ - b}{a}$