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Congratulations - you have completed Algebra: Quadratic Equations Test-3. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
Which of the following is a quadratic equation?
 A $\displaystyle {{x}^{\frac{1}{2}}}+2x+3=0$ B $\displaystyle \left( x-1 \right)\,\left( x+4 \right)={{x}^{2}}+1$ C $\displaystyle {{x}^{4}}-3x+5=0$ D $\displaystyle \left( 2x+1 \right)\,\left( 3x-4 \right)\,=2{{x}^{2}}+3$
Question 1 Explanation:
By observation the highest power of x is 2 only in option (d)
 Question 2
Which one of the following is a factor of
$\displaystyle {{x}^{3}}-19x+30$
 A $\displaystyle x-2$ B $\displaystyle x+2$ C $\displaystyle x-1$ D $\displaystyle x+1$
 Question 3
The solution of the equation
$\displaystyle \sqrt{25-{{x}^{2}}}=x-1$ are
 A $\displaystyle x=3\,\,\,and\,\,x=4$ B $\displaystyle x=5\,\,\,\,and\,\,\,\,x=1$ C $\displaystyle x=-3\,\,and\,\,x=4$ D $\displaystyle x=4\,\,\,\,and\,\,\,x\ne -3$
Question 3 Explanation:
For x =4 , the equation
$latex \sqrt{25-{{x}^{2}}}=x-1$ is satisfied ,
Thus options which can be correct are a, c and d. Now when we put x=-3 we find that both sides are not equal so we can conclude that (d) is the answer)
 Question 4
which is the one whose roots are 2 and −15?
 A $\displaystyle {{x}^{2}}-2x+15=0$ B $\displaystyle {{x}^{2}}+15x-2=0$ C $\displaystyle {{x}^{2}}+13x-30=0$ D $\displaystyle {{x}^{2}}-30=0$
Question 4 Explanation:
The factors are x-2 and x+15.
$\begin{array}{l}(x-2)(x+15)\\={{x}^{2}}+13x-30\end{array}$
 Question 5
If $\displaystyle \begin{array}{l}{{\left( a-3 \right)}^{2}}+{{\left( b-4 \right)}^{2}}+{{\left( c-9 \right)}^{2}}=0,\,\,\\then\,\,the\,\,value\,\,of\,\,\sqrt{a+b+c}\end{array}$ is
 A -4 B +4 C ±4 D ±2
Question 5 Explanation:
Since the sum of three squares can only be equal to 0
if the terms are individually equal to 0
we can conclude that a=3,b=4,c=9.
The sum of a, b, c = 16.
Thus, $\sqrt{a+b+c}=\sqrt{16}=\pm 4$
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