What is the solution for the equation [tex]7x - 3x^2 = 85 + 2x^2 + 2x[/tex]?
How do you solve it?
Answer (2)
7 x − 3 x 2 = 85 + 2 x 2 + 2 x 7 x − 3 x 2 − 85 − 2 x 2 − 2 x = 0 − 5 x 2 + 5 x − 85 = 0 ∣ d i v i d e e a c h t er m b y ( − 5 ) x 2 − x + 17 = 0 Δ = b 2 − 4 a c = ( − 1 ) 2 − 4 ⋅ 1 ⋅ 17 = 1 − 68 = − 67 A n s w er : I f Δ < 0 , t h e n roo t s a re ima g ina ry an d b eyo n d t h e sco p e o f t hi s b oo k
The equation 7 x − 3 x 2 = 85 + 2 x 2 + 2 x simplifies to x 2 − x + 17 = 0 . The discriminant calculated is − 67 , indicating there are no real solutions, and the roots are imaginary. Therefore, the equation has no real solutions.
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