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2 years ago

X squared + 3X -27/4 = 0

Mathematics

1 answer:

stepan [7]2 years ago

5 0

Answer:

Applying the quadratic formula.

Exact Form:

x=32,−92

Decimal Form:

x=1.5,−4.5

Mixed Number Form:

x=112,−412

Step-by-step explanation:

Solve the equation: x2 + 3x -27/4 = 0 With the coefficients: a = 1, b = 3, c = -6.75 a ≠ 0 With ∆ = 36> 0 => Equation has 2 distinct solutions

x1 = 1.5, x2 = -4.5

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Answer: a and c are polynomials, b is not.

Step-by-step explanation:

A polynomial p(x) is written as:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀*x⁰

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Notice that the powers need to be always natural numbers.

Now, let's analyze the options:

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We can rewrite this as:

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b) p² + 1/p (in this case the variable is p)

the second term can be written as:

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3 years ago

9/20

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Question:

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

Answer:

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Solution:

For a Quadratic Equation of form : $a x^{2}+b x+c=0$ ---- eqn 1

The solution is $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now , the given Quadratic Equation is $x^{2}+5 x+7=0$ ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , $b^2 - 4ac$ is called the discriminant of the quadratic equation

Its value determines the nature of roots

Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

$D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3$

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

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3 years ago

A man wants to hike two trails. The length of one trail is 7.709 km. The length of the other trail is 9.0309 km. What is the tot

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Step-by-step explanation:

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