2010004502
Level:
B
The quadratic equation
\[
ax^{2} + bx -24 = 0
\]
has solutions \(x_{1} = -2\)
and \(x_{2} = 4\). Find the
coefficients \(a\)
and \(b\).
\(a = 3\),
\(b = -6\)
\(a = -3\),
\(b = -6\)
\(a = -3\),
\(b = 6\)
\(a = 3\),
\(b = 6\)
Quadratic equations and inequalities
2010004501
Level:
B
One of the solutions of the quadratic equation \( x^{2} + 7x +c = 0\) is \(x_{1} = -3\). Find the second solution \(x_{2}\) and the value of the coefficient \(c\).
\(x_{2} = -4\) and
\(c = 12\)
\(x_{2} = 4\) and
\(c = -12\)
\(x_{2} = -4\) and
\(c = -12\)
\(x_{2} = 4\) and
\(c = 12\)
2000004905
Level:
A
From the given quadratic equations identify the one that has a double root.
\( x^2-10x+25=0\)
\( x^2-10x=0\)
\( x^2-10=0\)
\( x^2-10x+100=0\)
2000004904
Level:
A
From the given sets identify the one that contains all roots of the quadratic equation:
\[ x^2 =5\]
\( \left\{ -\sqrt{5}; \sqrt{5} \right\} \)
\( \left\{ 0; \sqrt{5} \right\} \)
\( \left\{\sqrt{5} \right\} \)
\( \left\{-5;5\right\}\)
2000004903
Level:
A
From the given sets identify the one that contains at least one root of the quadratic equation:
\[2x^2=18\]
\( \left\{-3; 1; \frac{1}{3}\right\}\)
\( \{0; 9; 27\}\)
\( \left\{-1;-\frac{1}{3};12\right\}\)
\(\left\{-9; -2; \frac{2}{3}\right\}\)
2000004902
Level:
A
Choose the equation that has two real roots and one of them is \(0\).
\( 3x^2 -10x=0\)
\( 3x^2 -10=0\)
\( 3x^2 +10=0\)
\( 10x^2=5\)
2000004901
Level:
A
Choose the equation that has no real roots.
\( 5x^2 +1 =0\)
\( 5x^2 +x =0\)
\( 5x^2 -1 =0\)
\( 5x^2 -x =0\)
2000001006
Level:
A
Find the solution set of the equation \(2(x-7)\left(x+\frac{1}{2}\right)=0\).
\(\left\{-\frac{1}{2};7\right\}\)
\(\left\{-7;\frac{1}{2}\right\}\)
\(\{-1;14\}\)
\(\{-14;1\}\)
2000001005
Level:
A
Find the solution set of the equation \(x^2 = 25\).
\(\{-5; 5\}\)
\(\{5\}\)
\(\{0; 5\}\)
\(\{-25; 25\}\)
2000001004
Level:
A
Find the solution set of the equation \(3x^2 + 15x = 0\).
\(\{-5; 0\}\)
\(\{ -5\}\)
\(\{0; 5\}\)
\(\left\{0; \frac{1}{5}\right\}\)