Question

Find the value of k for which x=-a is a zero of the polynomial x square + 4ax-k

Answer 1

⭐Hey here is your answer ⭐

X = -a

p(x) = x^2 + 4ax - k

p(-a) = (-a)^2 + 4.a.(-a) - k


a^2 - 4a^2 = k

-3a^2 = k


I HOPE IT WILL HELP YOU ☺️

Answer 2

Answer:

Concept:

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents, but not division by variable.

Step-by-step explanation:

The Fundamental Theorem of Algebra states that the degree of a polynomial determines how many zeros it will contain.

Given:

x = -a

Polynomial $x^{2} + 4ax - k$

Find:

Find the value of k

Solution:

Given Polynomial

         $x^{2} + 4ax - k$ = 0

Since −a is a zero of the given polynomial.

Therefore,

       $(-a)^{2}$ + 4 (a) (-a) - k = 0

       $a^{2}$ - 4 $a^{2}$ -k = 0

         - 3 $a^{2}$ - k = 0

                     k = -3 $a^{2}$

 So the value of k is -3 $a^{2}$

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