Help with precalculus please

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Find the equation (in slope -intercept form) for the line through (2,-5) that is parallel to 2x-3y=5.

Evaluate the discriminant for each equation, and use it to determine the number of real solutions to the equation. 2x^2-3x+10=0.

Find all real or imaginary solutions to each equation. Use the method of your choice on each problem. 2x^2-11x+5=0 and 2/x-2-3/x+2=1/2

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Explanation & Answer

 

2x^2-3x+10=0.

2) delta=(-3)²-4*2*10= 9 - 80 = - 71 <0  so inexeste solution in IR 

3)  2x^2-11x+5=0  so delta= (-11)²- 4*2*5 = 81 > 0 

so ::  x1 = (11 - sqrt(81))/4 =  2/4 = 1/2 

         x2 = (11 + sqrt(81))/4 = 20/4 =

for : 2/x-2-3/x+2=1/2  =>  x²+2x-22=0 

so delta= 2² + 88 = 92

x1= (-2- sqrt(92))/2

x1= (-2+ sqrt(92))/2


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