Quadratic inequality solving

Solve the quadratic inequality: -2x2 + 4x + 6 <0

Result

O : (Correct answer is: ) OK

Step-by-step explanation:

−2x2 + 4x + 6 < 0 2x2 − 4x − 6 > 0  2x2−4x−6=0  2x2−4x−6=0 2 ...  prime number 4=22 6=2⋅3 GCD(2,4,6)=2  x2−2x−3=0  a=1;b=−2;c=−3 D=b2−4ac=22−4⋅1⋅(−3)=16 D>0  x1,2​=2a−b±D​​=22±16​​ x1,2​=22±4​ x1,2​=1±2 x1​=3 x2​=−1  (x−3)(x+1)>0  x>3 ∧ x > −1 x<3 ∧ x < −1  x>3   ∨ x < −1  O=R − <−1; 3 >

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