Write "True" if the statement is correct or "false "if it is incorrect on the space provided. $$ \qquad $$ 1. If the discriminate $$ D=b^{2}-4 a c0 $$, then the quadratic equation $$ a x^{2}+b x+c=0, a eq 0 $$ has two distininct roots, $$ \qquad $$ 2. The solution set of $$ 2 x^{2}-5 x+2=0 $$ is $$ \left\{\frac{1}{2}, 2 ight\} $$. $$ \qquad $$ 3. The solution set $$ |3 x-1|

Question

Write "True" if the statement is correct or "false "if it is incorrect on the space provided. $$ \qquad $$ 1. If the discriminate $$ D=b^{2}-4 a c>0 $$, then the quadratic equation $$ a x^{2}+b x+c=0, a eq 0 $$ has two distininct roots, $$ \qquad $$ 2. The solution set of $$ 2 x^{2}-5 x+2=0 $$ is $$ \left\{\frac{1}{2}, 2 ight\} $$. $$ \qquad $$ 3. The solution set $$ |3 x-1|<0 $$ is the set of real numbers. $$ \qquad $$ 4. If the absolute value greater than or equal to zero, then the solution set is the set of real numbers. $$ \qquad $$ 5. The solution set of $$ x^{2}-x \geq 12 $$ is $$ [-3,12] $$ II. Choose the correct answer from the given alternatives and write the letter of your correct choice space provided. $$ \qquad $$ 6. If xis a natural number then the solution set for inequality $$ 3 x+7<6 $$ is A. $$ (1,2) $$ B. $$ [2,3] $$ C. $$ (-0,1,2,3) $$ D. $$ (4,5,6,-) $$ $$ \qquad $$ 7. Which of the following is the solution for the inequality $$ |3 x+7| \leq 5 $$ ? A $$ \frac{2}{3} \leq x \leq 4 $$ B. $$ x \leq \frac{-2}{3} $$ C. $$ x \leq-4 $$ D. $$ 4 \leq x \leq \frac{-2}{3} $$ $$ \qquad $$ 8. Which of the following point is a eolution to the inequality $$ \left\{\begin{array}{l}x-2 y>-1 \ 3 x-y<-3\end{array} ight. $$ ? A. $$ (2,1) $$ B. $$ (-2,-1) $$ D. $$ (-2,-1) $$ $$ \qquad $$ 9. Which of the following is not true? For appositive real number a A. The eolution of $$ |x|a $$ means $$ x>a $$ or $$ x<-a $$ D. The solution of $$ |x|<0 $$ is the sot of roal number $$ \qquad $$ 10. What is the solution set of $$ 2 x^{2}+4 x+1=0 $$ A. $$ \left\{\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} ight\} $$ B. $$ \left\{-1 \frac{\sqrt{2}}{2},-1+\frac{\sqrt{2}}{2} ight] $$ C. $$ \odot $$ D. $$ (-1+\sqrt{2}, 1-\sqrt{2}) $$ $$ \qquad $$ C. 3 $$ \qquad $$ A. 4 B. -4 $$ \qquad $$ 12. From question number 11 what is the velue of $$ k $$ ? B. 14 C. 3.5 D. -3.5 $$ \qquad $$ A. 7 13 3. What is the dimession of rectangle whose perimetere is 26 cm and, whose area is D. None $$ 40 \mathrm{~cm}^{2} $$ C. 11 and 15 A. 8 and 5 B. 7 and 6 $$ \qquad $$ 14. What is the solution set of $$ |2 x-16| \leq 0 $$ C. $$ (-\infty, \infty) $$ D. $$ (0) $$ A. 0 B. $$ { }^{8} 8 $$

UpStudy AI · Accepted Answer

1. $$D=b^2-4ac>0$$ guarantees that
$$
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
$$
yields two different real numbers.  
Answer: True

2. For 
$$
2x^2-5x+2=0,
$$
the discriminant is 
$$
(-5)^2-4\cdot2\cdot2=25-16=9.
$$
The roots are 
$$
x=\frac{5\pm3}{4}=\frac{8}{4}\text{ or }\frac{2}{4},
$$
i.e. $$x=2$$ or $$x=\tfrac{1}{2}$$.  
Answer: True

3. The inequality
$$
|3x-1|<0
$$
has no solution because for any real number $$x$$ we have $$|3x-1|\ge0$$ and the strict inequality cannot hold.  
Answer: false

4. Since for every real number $$x$$
\[
|\,\text{(anything)}\,|\ge0,
\
1. True 2. True 3. False 4. True

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