1) 4x²+5x-6=0
2) 4x²-2x+0.25=0
3)3x²+4x+5=0

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вопрос

1) For the first equation, we can use the quadratic formula to find the roots. The formula is: x = (-b ± √(b² - 4ac)) / 2a.
Plugging in the values from the equation 4x²+5x-6=0, we have a=4, b=5, and c=-6.
x = (-5 ± √(5² - 44(-6))) / (2*4)
x = (-5 ± √(25 + 96)) / 8
x = (-5 ± √121) / 8
x = (-5 ± 11) / 8
x = -16/8 or x = 6/8
x = -2 or x = 0.75
Therefore, the roots of the equation 4x²+5x-6=0 are x = -2 and x = 0.75.

2) For the second equation, 4x²-2x+0.25=0, we can also use the quadratic formula to find the roots. The value of a=4, b=-2, c=0.25.
x = (2 ± √((-2)² - 440.25)) / 8
x = (2 ± √(4 - 4)) / 8
x = (2 ± 0) / 8
x = 2/8
x = 0.25
Therefore, the only root of the equation 4x²-2x+0.25=0 is x = 0.25.

3) For the third equation, 3x²+4x+5=0, we can again use the quadratic formula to find the roots. The value of a=3, b=4, c=5.
x = (-4 ± √(4² - 435)) / 2*3
x = (-4 ± √(16 - 60)) / 6
x = (-4 ± √(-44)) / 6
x = (-4 ± 2√11i) / 6
x = (-2 ± √11i) / 3
Therefore, the roots of the equation 3x²+4x+5=0 are x = (-2 + √11i)/3 and x = (-2 - √11i)/3, where i is the imaginary unit.