Algebra

\(f(x)=5x^2 - 2x + 8 - 2x^2 + 6x + 2\\ f(x)=3x^2+4x+10=0\\ \)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ b^2-4ac=16-4\cdot 3\cdot 10=-104\\ (b^2-4ac)<0\)

The discriminant is less than zero. The function has no zero, no solution.

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Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2.     

When a quadratic is arranged in standard format, ax² + bx + c = 0,    

the discriminant is given by b² – 4ac.    

Combine like terms in the quadratic of interest and arrange in standard format.    

3x² + 4x + 10   

b² – 4ac    

4² – (4)(3)(10)    

16 – 120    

–104 is the discriminant    

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