What is the value of the discriminant for the quadratic equation $-3=-x+2 x$?

Discriminant $=b^2-4 a c$

Rewrite the equation in standard form: 2 x 2 − x + 3 = 0 .
Identify the coefficients: a = 2 , b = − 1 , c = 3 .
Calculate the discriminant using the formula D = b 2 − 4 a c .
The discriminant is D = ( − 1 ) 2 − 4 ( 2 ) ( 3 ) = 1 − 24 = − 23 , so the final answer is − 23 ​ .

Explanation

Rewrite the equation First, we need to rewrite the given equation in the standard quadratic form, which is a x 2 + b x + c = 0 . The given equation is − 3 = − x + 2 x 2 .

Standard form Rearranging the terms, we get 2 x 2 − x + 3 = 0 .

Identify coefficients Now, we can identify the coefficients: a = 2 , b = − 1 , and c = 3 .

Calculate the discriminant The discriminant is given by the formula D = b 2 − 4 a c . Substituting the values of a , b , and c , we get: D = ( − 1 ) 2 − 4 ( 2 ) ( 3 ) D = 1 − 24 D = − 23

Final Answer Therefore, the value of the discriminant is -23.


Examples
The discriminant helps determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has one real root (a repeated root). If it is negative, the equation has two complex roots. For example, in engineering, when designing a bridge, the quadratic equation might represent the stress on a support beam. The discriminant would then tell you whether the beam will withstand the stress (real roots) or fail (complex roots).

Answered by GinnyAnswer | 2025-07-03

The discriminant of the quadratic equation − 3 = − x + 2 x 2 is found by rewriting the equation in standard form and calculating using D = b 2 − 4 a c . Upon calculation, the value of the discriminant is − 23 , indicating that the roots are complex. Therefore, the final answer is − 23 ​ .
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Answered by Anonymous | 2025-07-04