Question

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

Answers

  2. Answer:

    \boxed {\boxed {\sf 1 \ real \ root}}

    Step-by-step explanation:

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

    x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}

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

    • Negative: there are no real roots
    • Zero: there is one real root
    • Positive: there are two real roots

    It is the expression under the square root symbol:

    b^2-4ac

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

    ax^2+bx+c=0

    The equation given is x^2 +14x= -49. We have to move the -49 to the left side. Since it is a negative number, we add 49 to both sides.

    x^2+14x+49 = -49 +49 \\x^2+14x+49=0

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

    • a= 1
    • b= 14
    • c= 49

    Substitute these values into the formula for the discriminant.

    (14)^2 -4 (1)(49)

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

    Solve the exponent.

    • (14)²= 14 * 14= 196

    196- 4(1)(49)

    Multiply 4, 1, and 49.

    196-196

    Subtract.

    0

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

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