Coaching Centre
The discriminant
The discriminant Δ = b² − 4ac and how it tells the number and type of solutions of a quadratic equation.
The discriminant
The number of solutions equals the number of times the parabola meets the x-axis.
How many solutions does $x^2 + 4x + 5 = 0$ have?
For what value of $k$ does $x^2 + 6x + k = 0$ have exactly one solution?
Discriminant of $x^2 + 4x + 5$?
$16 - 20$.
$x^2 + 6x + k = 0$ has one solution. Find $k$.
$36 - 4k = 0$.
Number of real solutions of $x^2 + 4x + 5 = 0$?
$\Delta < 0$.
Number of solutions of $x^2 - 6x + 9 = 0$?
$\Delta = 0$.
Number of solutions of $2x^2 - 3x - 4 = 0$?
$\Delta = 41 > 0$.
$\Delta = 49$. The solutions are:
$49$ is a perfect square.
$x^2 + bx + 4 = 0$ has no real solutions when:
$9 - 16 < 0$.
Discriminant of $3x^2 + x - 2$?
$1 + 24$.
New numbers every time. Keep going until you get five in a row.