What is the value of the discriminant for the quadratic equation [tex]$0=2 x^2+x-3$[/tex]?
Discriminant = [tex]$b^2-4 a c$[/tex]
A. -25
B. -23
C. 25
D. 26
Answer (2)
Identify the coefficients: a = 2 , b = 1 , c = − 3 .
Apply the discriminant formula: D = b 2 − 4 a c .
Substitute the values: D = ( 1 ) 2 − 4 ( 2 ) ( − 3 ) .
Calculate the discriminant: D = 25 . The value of the discriminant is 25 .
Explanation
Understanding the problem We are given the quadratic equation 0 = 2 x 2 + x − 3 . We need to find the value of the discriminant.
Recalling the discriminant formula The discriminant of a quadratic equation in the form a x 2 + b x + c = 0 is given by the formula D = b 2 − 4 a c .
Identifying the coefficients In our equation, we can identify the coefficients as follows: a = 2 b = 1 c = − 3
Substituting the values Now, we substitute these values into the discriminant formula: D = b 2 − 4 a c = ( 1 ) 2 − 4 ( 2 ) ( − 3 )
Calculating the discriminant Calculating the discriminant: D = 1 − 4 ( 2 ) ( − 3 ) = 1 − ( − 24 ) = 1 + 24 = 25
Examples
The discriminant helps determine the nature of the roots of a quadratic equation. For example, in engineering, when designing a bridge, the equation describing the load distribution might be quadratic. The discriminant helps engineers determine if the bridge design will have real solutions (stable) or complex solutions (unstable), ensuring the bridge's safety and stability. Similarly, in physics, when analyzing projectile motion, the discriminant can tell us whether a projectile will hit a target or not, based on the initial conditions.
The value of the discriminant for the quadratic equation 0 = 2 x 2 + x − 3 is 25 , indicating two distinct real roots. The calculation involves identifying coefficients and substituting them into the discriminant formula. The answer is C .25 .
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