Question

what constant should be added to the polynomial x²+7x+5 so that -2 is zero of resulting polynomial​

Answer 1

Answer:

The required constant is 5

Step-by-step explanation:

Let,

$f(x) = x^2 + 7x+5$

and the resulting polynomial be $g(x)$

given that, $g(-2) =0$

let, $g(x) = f(x) +c$   (where $c$ is the required constant)

On putting x = -2 we get

$g(-2) = f(-2) +c\\or, 0 = (-2)^2 + 7(-2) + 5 +c\\or,4-14+5+c = 0\\or, c = 5$

Answer 2

SOLUTION

TO DETERMINE

The constant should be added to the polynomial x² + 7x + 5 so that - 2 is zero of resulting polynomial

EVALUATION

Here the given polynomial is

x² + 7x + 5

Let k be the constant should be added to the polynomial x² + 7x + 5 so that - 2 is zero of resulting polynomial

Let p(x) be the resulting polynomial

Then p(x) = x² + 7x + 5 + k

So by the given condition

$\sf p( - 2) = 0$

$\displaystyle \sf{ \implies {( - 2)}^{2} + 7 \times ( - 2) + 5 + k = 0}$

$\displaystyle \sf{ \implies 4 - 14 + 5 + k = 0}$

$\displaystyle \sf{ \implies k - 5= 0}$

$\displaystyle \sf{ \implies k = 5}$

Hence the required constant = 5

FINAL ANSWER

The constant 5 should be added to the polynomial x² + 7x + 5 so that - 2 is zero of resulting polynomial

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If p(x) = 2x2 + 4x + 6 is a quadratic polynomial then what is the value of sum of zeroes?

https://brainly.in/question/31024345

2. write a quadratic polynomial sum of whose zeroes is 2 and product is -8

https://brainly.in/question/25501039