Answer:
2 real different roots
Step-by-step explanation:
Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:
[tex]\displaystyle{D = b^2-4ac}[/tex]
The formula is derived from a quadratic formula which is:
[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The expression inside the square root is discriminant. The discriminant says that:
- There are 2 real different roots if the discriminant (D) is greater than 0. (D > 0)
- There is 2 real double roots (same roots) if the discriminant (D) is equal to 0. (D = 0)
- There are no real roots (imaginary or complex roots) if the discriminant (D) is less than 0. (D < 0)
From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:
Therefore, substitute the coefficients’ values in the discriminant:
[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]
Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.
