Question

If zeroes of the quadratic polynomial: ax2 +bx+c is negative reciprocal of each other ,then find the relationship between a and c.

Answer 1

Answer:

Step-by-step explanation:

Zeros of polynomial  are reciprocal of each other.

Solution:

One zero of the polynomial  is reciprocal of the other.

Assume that one of the zero of above polynomial as x, then another zero will be 1/x.

Product of zeroes  

Let us take one polynomial to find that when a = c, zeros are reciprocal.

First zero = x + 2 i.e. x = -2

Second zero = 4x + 2 i.e. 4x = -2 then x = -1/2

Hence, it can be said that a = c, then zeros are reciprocal.

Answer 2

Answer:

the relationship between a and c is $c=a$

Step-by-step explanation:

Given: Polynomial function, $p(x)=ax^{2} +bx+c$

Find: The relationship between a and c.

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0.

Now,

Given quadratic polynomial is $p(x)=ax^{2} +bx+c$

Let the roots be $\alpha$ and $\frac{1}{\alpha}$ as roots are reciprocal.

Products of roots $=\frac{c}{a}$

$\Rightarrow \alpha \times\frac{1}{\alpha} =\frac{c}{a}$

$\Rightarrow 1=\frac{c}{a} \\\Rightarrow c=a$

Hence the relationship between c and a is that they are equal.

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