Question

Form a quadratic polynomial whose sum of zeros is 8 and the product is -56

Answer 1

SOLUTION

TO DETERMINE

The quadratic polynomial whose sum of zeros is 8 and the product is -56

FORMULA TO BE IMPLEMENTED

The quadratic polynomial whose sum of zeros and product of zeros are given can be written as

$\sf{ {x}^{2} - (sum \:of \:the \: zeros)x + (product \:of \:the \: zeros) }$

EVALUATION

Here it is given that the quadratic polynomial is the polynomial whose sum of zeros is 8 and the product is -56

The required Quadratic polynomial is

$\sf{ {x}^{2} - (sum \:of \:the \: zeros)x + (product \:of \:the \: zeros) }$

$= \sf{ {x}^{2} - 8x - 56 }$

FINAL ANSWER

The quadratic polynomial whose sum of zeros is 8 and the product is -56

$= \sf{ {x}^{2} - 8x - 56 }$

ADDITIONAL INFORMATION

A general equation of quadratic equation is

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

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

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

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

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Answer 2

GIVEN :

The sum of zeros is 8 and the product is -56

TO FIND :

A quadratic polynomial with sum of zeros is 8 and the product is -56

SOLUTION :

Given that for a quadratic polynomial whose sum of zeros is 8 and the product is -56

From the given sum of zeros = 8 and  the product of the zeros =-56

The formula for a quadratic polynomial with sum of the zeros and product of the zeros is given by,

$x^2-(sum of the zeros)x+product of the zeros=0$

By substituting the values  we get,

$x^2-(8)x+(-56)=0$

$x^2-8x-56=0$

∴ a quadratic polynomial with sum of zeros is 8 and the product is -56  is $x^2-8x-56=0$