Question

If one zero of the polynomial f(x)= 5x² +13x +k is the reciprocal of the other, then
the value of k is 5. true or false​

Answer 1

Answer:

Given :-

• f(x)= 5x² +13x +k

Find :

• Is the given zero is correct Or not.

Solution :

For checking whether it is the zero Or not :-

Let us we consider the zero be ' alpha '

According to the Question :-

Other one is reciprocal of it i. e, $:\implies\bf{\dfrac{1}{\alpha}}$

Now,

Given polynomial :

p(x) = 5x² + 13x + k

Comparing it with the General form of quadratic Equation.

$:\implies\bf{ax^{2} + bx + c}$

We got,

$:\implies\sf{a = 5}$

$:\implies\sf{b = 13}$

$:\implies\sf{c = k}$

Now,

Product of zeroes =

$:\implies\bf{\dfrac{Constant}{Coeficient\: of \: x^{2}}}$

Putting up the values :

$\alpha$ + ${\dfrac{1}{\alpha}}$ = $\bf{\dfrac{k}{5}}$

→ 1 = $\sf{\dfrac{k}{5}}$

→ 5 = k

Hence, The given zero is 5

This statement is True.