Question

if 5 is the zero of x^3+kx^2+2x+8 find k

Answer 1

p(x) = x³ + kx² + 2x + 8

p(5) = 0

p(5) = 5³ + 25k + 10 + 8

125 + 25k + 18 = 0

143 + 25k = 0

25k = -143

k = -143/25

Answer 2

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. x²+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x², x, and -12.

Given:

5 is the zero of x^3+kx^2+2x+8 find k

Find:

Find k

Solution:

p(x) = x³ + kx² + 2x + 8

∵ p(5) = 0

p(5) = 5³ + 25k + 10 + 8

⇒125 + 25k + 18 = 0

⇒143 + 25k = 0

⇒25k = -143

⇒ k = -143/25

Therefore, value of k is -143/25

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