Question

if the sum of the roots is -p and product of the roots is -1/p, then the quadratic polynomial is​

Answer 1

Answer:

x²- (-p)x + (-1/p) = 0

= x² + px -1/p = 0

Multiple equation by p

= p (x² + px -1/p = 0)

= px² + p²x - 1 = 0

I HOPE THIS WILL HELP YOU

Answer 2

Given: The sum of the roots is -p and product of the roots is -1/p.

To find: The quadratic polynomial

Solution: A quadratic polynomial is a polynomial which has at most 2 roots since there are at most 2 values at which the value of the polynomial can be 0.

Let the roots of the quadratic polynomial be a and b.

Therefore,

Sum of roots

= a+b

= -p

Product of roots

=a × b

= -1/p

Now, any quadratic polynomial whose sum and product of zeroes are known can be written as:

${x}^{2} - (sum \: of \: roots)x + product \: of \: roots$

Using the values:

${x}^{2} - ( - p)x + ( - \frac{1}{p} )$

$= {x}^{2} + px - \frac{1}{p}$

Therefore, the quadratic polynomial whose sum and product of roots are -p and -1/p respectively is ${x}^{2} + px - \frac{1}{p}$.