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3 years ago

Use the Zero Product Property to find the x-intercepts for x^2+6x=y

Mathematics

1 answer:

Semmy [17]3 years ago

4 0

Answer:

$x=0\ or\ x =-6$

Step-by-step explanation:

Given

$x^2+6x=y$

Required

Determine the x intercepts

To get the x intercepts, we simply set y to 0

Substitute 0 for y;

$x^2+6x=0$

Factorize:

$x(x +6) = 0$

Apply zero product property

$x=0\ or\ x + 6 =0$

$x=0\ or\ x =-6$

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3 years ago

Read 2 more answers

X-y=5 and x^2y=5x+6

sergeinik [125]

By applying algebraic handling on the two equations, we find the following three <em>solution</em> pairs: x₁ ≈ 5.693 ,y₁ ≈ 10.693; x₂ ≈ 1.430, y₂ ≈ 6.430; x₃ ≈ - 0.737, y₃ ≈ 4.263.

<h3>How to solve a system of equations</h3>

In this question we have a system formed by a <em>linear</em> equation and a <em>non-linear</em> equation, both with no <em>trascendent</em> elements and whose solution can be found easily by algebraic handling:

x - y = 5 (1)

x² · y = 5 · x + 6 (2)

By (1):

y = x + 5

By substituting on (2):

x² · (x + 5) = 5 · x + 6

x³ + 5 · x² - 5 · x - 6 = 0

(x + 5.693) · (x - 1.430) · (x + 0.737) = 0

There are three solutions: x₁ ≈ 5.693, x₂ ≈ 1.430, x₃ ≈ - 0.737

And the y-values are found by evaluating on (1):

y = x + 5

x₁ ≈ 5.693