Question

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

1. Step-by-step explanation:

2. thienthi 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…

• 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: 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:

• a= 1
• b= 14
• c= 49

Substitute these values into the formula for the discriminant. Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve the exponent.

• (14)²= 14 * 14= 196 Multiply 4, 1, and 49. Subtract. The discriminant is zero, so the quadratic equation x²+ 14x = -49  has 1 real root.