Answer:

1: (-infinity, 1) and (2, +infinity)

solution = First solve f(x) = x^2 - 3x + 2 = 0

Since (a + b + c = 0), use the Shortcut. The 2 real roots are x = 1 and x = c/a = 2.

Use the algebraic method to solve f(x) > 0. Since a > 0, the parabola opens upward. Inside the interval (1, 2), f(x) is negative. Outside the interval (1, 2), f(x) is positive.

Answer by open intervals: (-infinity, 1) and (2, +infinity)

graph{x^2 - 3x + 2 [-10, 10, -5, 5]}

2: x=−102=−5 solution = that:

x=−b±√b2−4ac2a

Where ax2+bx+c=0.

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In this case, a=1, b=10, and c=25. Now all we have to do is plug these values into the quadratic formula and simplify it.

x=−b±√b2−4ac2a

x=−10±√102−4(1)(25)2(1)

x=−10±√100−1002

x=−10±02

3:

x=−52±√332 solution =

y=x2+5x−2=0

y=x2+5x−2=0D=d2=b2−4ac=25+8=33 -->d=±√33

y=x2+5x−2=0D=d2=b2−4ac=25+8=33 -->d=±√33There are 2 real roots.

y=x2+5x−2=0D=d2=b2−4ac=25+8=33 -->d=±√33There are 2 real roots.x=−b2a±d2a=−52±√332