# Test: Quadratic Functions III - Challenging

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Question 1:   Solve the equation  ${x}^{2}-\frac{9x}{\left|x\right|}=0$
${x}_{1,2}=±3$
$х=-3$
$х=9$
$х=3$
Question 2:   Solve the equation  ${x}^{2}-5\sqrt{{x}^{2}}+4=0$
$x=4,\text{\hspace{0.17em}}x=1$
$x=±4,\text{\hspace{0.17em}}x=±1$
$x=±4$
$\text{\hspace{0.17em}}x=±1$
Question 3:   Solve the equation  ${x}^{2}-12{\left(\sqrt{x}\right)}^{2}-28=0$
$х=14,\text{\hspace{0.17em}}х=-2$
$х=-14,\text{\hspace{0.17em}}х=2$
$х=14$
$х=-2$
Question 4:   Solve the equation  ${x}^{2}-3x+\frac{7}{x-2}=\frac{7}{x-2}-2$
$х=-1$
$х=1$
$х=2$
$x=2,\text{​}\text{\hspace{0.17em}}\text{​}\text{​}\text{​}\text{​}\text{​}\text{​}х=1$
Question 5:   Which quadratic equation corresponds to the below graph? ${x}^{2}-6x+5=0$
${x}^{2}-3x+5=0$
${x}^{2}-6x=0$
${x}^{2}-6x+4=0$
Question 6:   Which quadratic equation corresponds to the below graph? $-{x}^{2}+9x-14=0$
$-{x}^{2}+9x-5=0$
$-{x}^{2}+9x=0$
${x}^{2}-9x+14=0$
Question 7:   For what value of  $b$  the equation  $4{х}^{2}-bx+20=0$  has only one square root?
$b=\sqrt{5}$
$b=±8\sqrt{5}$
$b=-8\sqrt{5}$
$b=8\sqrt{5}$
Question 8:   What is a sign of a coefficient  $а$  and discriminant of the quadratic equation represented by the following graph: $a<0,\text{\hspace{0.17em}}D>0$
$a<0,\text{\hspace{0.17em}}D<0$
$a>0,\text{\hspace{0.17em}}D<0$
$a>0,\text{\hspace{0.17em}}D>0$
Question 9:   Based on the Vietaâ€™s Theorem find  ${x}_{1}^{2}+{x}_{2}^{2}$ ,  when  ${х}_{1}$  and  ${х}_{2}$  are square roots of  $3{x}^{2}-x+10=0$
$\frac{22}{9}$
$\frac{7}{9}$
$1$
$-6\frac{5}{9}$
Question 10:   Based on the Vieta's Theorem find  $\left|{х}_{2}-{х}_{1}\right|$ ,  when  ${х}_{1}$  and  ${х}_{2}$  are square roots of  ${x}^{2}-5x+6=0$
$1$
$±1$
$0$
$2$