Which of the following is a quadratic equation?
\(x^2+2x+1=(4-x)^2+3\)
\(-2x^2=(5-x)\left(2x-\dfrac{2}{5}\right)\)
\((k+1)x^2+\dfrac{3}{2}x=7,\; k=-1\)
\(x^3-x^2=(x-1)^3\)
Which of the following is not a quadratic equation?
\(2(x-1)^2=4x^2-2x+1\)
\(2x-x^2=x^2+5\)
\((\sqrt{2}x+\sqrt{3})^2+x^2=3x^2-5x\)
\((x^2+2x)^2=x^4+3+4x^3\)
Which equation has \(2\) as a root?
\(x^2-4x+5=0\)
\(x^2+3x-12=0\)
\(2x^2-7x+6=0\)
\(3x^2-6x-2=0\)
If \(\dfrac{1}{2}\) is a root of \(x^2+kx-\dfrac{5}{4}=0\), the value of \(k\) is
2
−2
\(\dfrac{1}{4}\)
\(\dfrac{1}{2}\)
Which equation has the sum of its roots equal to \(3\)?
\(2x^2-3x+6=0\)
\(-x^2+3x-3=0\)
\(\sqrt{2}\,x^2-\dfrac{3}{\sqrt{2}}x+1=0\)
\(3x^2-3x+3=0\)
Values of \(k\) for which \(2x^2-kx+k=0\) has equal roots are
0 only
4
8 only
0, 8
Which constant must be added and subtracted to complete the square in \(9x^2 + \dfrac{3}{4}x - \sqrt{2} = 0\)?
\(\dfrac{1}{8}\)
\(\dfrac{1}{64}\)
\(\dfrac{1}{4}\)
\(\dfrac{9}{64}\)
The quadratic \(2x^2-\sqrt{5}\,x+1=0\) has
two distinct real roots
two equal real roots
no real roots
more than two real roots
Which equation has two distinct real roots?
\(2x^2-3\sqrt{2}x+\dfrac{9}{4}=0\)
\(x^2+x-5=0\)
\(x^2+3x+2\sqrt{2}=0\)
\(5x^2-3x+1=0\)
Which equation has no real roots?
\(x^2-4x+3\sqrt{2}=0\)
\(x^2+4x-3\sqrt{2}=0\)
\(x^2-4x-3\sqrt{2}=0\)
\(3x^2+4\sqrt{3}x+4=0\)
\((x^2+1)^2-x^2=0\) has
four real roots
two real roots
no real roots
one real root