## Inquiry

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# Quadratic Equation - Roots Properties

1. Find out a quadratic equation in form x^{2} +px +q = 0 so that p = -(x_{1}+x_{2}) and q = x_{1}.x_{2} :

2. For which „k“ one root of the equation x^{2}-5x+k=0 equals x_{1}=3?

3. For which „k“ one root of the equation kx^{2}-15x+7=0 equals x_{1}=7?

4. For which „k“ one root of the equation x^{2}+kx+20=0 equals x_{1}=10?

5. For which „a“ the equations‘ roots fit the relation x^{2}-3ax-4a^{2}=0 and x_{1}-x_{2}=10?

6. For which „m“ real numbers does the equation x^{2}+3x-2m^{2}+m+3=0 have one zero root? What is the second root?

7. For the equation x^{2}-13x+36=0 find out an equation with roots y_{1},y_{2} which fit following relations:

8. For the equation x^{2} – 6x +8 = 0 find out an equation with roots that fit following relations:

Solution:

9. The equation x^{2}–x .cos α + cos 2α = 0 has roots x_{1} , x_{2}. Express the relation:

Solution:

10. Let x_{1} and x_{2} be the roots of the equation 2x^{2} + 1,1x - 3,91 = 0. Find out (x_{1} – x_{2})^{2}, not solving the equation.

Solution: