1003124103
Level:
B
The following equation has roots \( -1 \) and \( 5 \). Find the value of the constant \( c \).
\[ x^2-4x+c=0 \]
\( -5 \)
\( 4 \)
\( -1 \)
\( 1 \)
Quadratic equations and inequalities
1003124102
Level:
B
The following equation has roots \( -\sqrt3 \) and \( \sqrt3 \). Find the value of the linear coefficient \( b \).
\[ x^2+bx+c=0 \]
\( 0 \)
\( 1 \)
\( 3 \)
\( -3 \)
1003124101
Level:
B
The following equation has roots \( -4 \) and \( 2 \). Find the value of the linear coefficient \( b \).
\[ x^2+bx-8=0 \]
\( 2 \)
\( 4 \)
\( 1 \)
\( -2 \)
1003123807
Level:
A
Choose the interval in which at least one root of the following equation lies.
\[ x^2-8=0 \]
\( [ 2;3 ] \)
\( [ 3;4 ] \)
\( [ -1;1 ] \)
\( [ -8;-5 ] \)
1003123806
Level:
A
Choose the interval in which all the roots of the following equation lie.
\[ 5x^2-7x=0 \]
\( \left[-\frac75;\frac75\right] \)
\( \left[-1;1\right] \)
\( ( 0;2] \)
\( \left[-\frac75;0\right] \)
1003123805
Level:
A
Choose the equation which has the double root equal to zero.
\( 2x^2=0 \)
\( x^2+x=0 \)
\( x^2-x=0 \)
\( -x^2+x=0 \)
1003123804
Level:
A
Choose the equation which has no real roots.
\( 4x^2+16=0 \)
\( -4x^2+16=0 \)
\( 16x^2-4=0 \)
\( \sqrt2x^2-2=0 \)
1003123803
Level:
A
Choose the equation which has at least one root in \( (2; 3) \).
\( 2x^2-9=0 \)
\( 2x^2+9=0 \)
\( 3x^2-9=0 \)
\( x^2-9=0 \)
1003123802
Level:
A
Choose the equation which has at least one root in \( (0;1] \).
\( 4x^2-3x=0 \)
\( 3x^2-4x=0 \)
\( 4x^2+3x=0 \)
\( 3x^2+4x=0 \)
1003123801
Level:
A
Choose the equation which has no real roots.
\( x^2+\sqrt2=0 \)
\( x^2+\sqrt2 x=0 \)
\( x^2-\sqrt2=0 \)
\( x^2-\sqrt2 x=0 \)