Determine the number of roots the equation x^2+14x=-49 using the discriminant.

Step-by-step explanation:

The quadratic formula is used to find the roots or zeroes of a quadratic equation. It is:

The discriminant helps us find the number of roots. If the discriminant is...

It is the expression under the square root symbol:

First, we must put the given quadratic equation into standard form, which is:

The equation given is . We have to move the -49 to the left side. Since it is a negative number, we add 49 to both sides.

Now we can solve for the discriminant because we know that:

Substitute these values into the formula for the discriminant.

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve the exponent.

Multiply 4, 1, and 49.

Subtract.

The discriminant is zero, so the quadratic equation x²+ 14x = -49  has 1 real root.

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

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step-by-step explanation: