Question

A) Find a polynomial, which, when added to the polynomial 5x2–3x–9, is equivalent to: 18

Answer 1

Answer:

(a) $-5x^2+3x+27$

(b)  $-5x^2+3x+9$

Step-by-step explanation:

(a)

Let the polynomial be Q(x).

Given polynomial P(x) = $5x^2-3x-9$

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial $5x^2-3x-9$, is equivalent to 18.

$P(x)+Q(x) = 18$

$5x^2-3x-9 +Q(x) = 18$

⇒$Q(x) = 18 -(5x^2-3x-9)$

or

$Q(x) = 18 -5x^2+3x+9$

Simplify:

$Q(x) =-5x^2+3x+27$

Therefore, the polynomial is,  $-5x^2+3x+27$

Check:

$P(x)+Q(x)$ = $5x^2-3x-9 +(-5x^2+3x+27)$

                      = $5x^2-3x-9 -5x^2 +3x+27$

                       = 18

(b)

Let the polynomial be Q(x).

Given polynomial P(x) = $5x^2-3x-9$

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial $5x^2-3x-9$, is equivalent to 0.

$P(x)+Q(x) = 0$

$P(x) = -Q(x)$

⇒$Q(x) = -(5x^2-3x-9)$

or

$Q(x) = -5x^2+3x+9$

Therefore, the polynomial is,  $-5x^2+3x+9$

Check:

$P(x)+Q(x)$=$5x^2-3x-9 +(-5x^2+3x+9)$

                      = $5x^2-3x-9-5x^2 +3x+9$

                       = 0

Answer 2

Answer:

a) $-5x^{2}+3x+27$

b) $-5x^{2}+3x+9$

Step-by-step explanation:

a) Let the required polynomial be p(x).

We have the relation, $5x^{2}-3x-9$ + p(x) = 18

i.e. p(x) = 18 $-5x^{2}+3x+9$

i.e. p(x) = $-5x^{2}+3x+27$

b) Let the required polynomial be q(x).

We have the relation, $5x^{2}-3x-9$ + q(x) = 0

i.e. q(x) = 0 $-5x^{2}+3x+9$

i.e. q(x) = $-5x^{2}+3x+9$