Advertisements
Advertisements
प्रश्न
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
Advertisements
उत्तर
x2 +4x +k=0
∴ Roots of given equation are real,
D≥0
implies that
(4)2 - 4 ×k ≥ 0
implies that
-4k ≥ -16
implies that
k ≤ 4
∴ k has all real values k ≤ 4.
APPEARS IN
संबंधित प्रश्न
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2 - 2sqrt(ac)x + b = 0` are simultaneously real, then prove that b2 = ac.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
(x2 + 1)2 – x2 = 0 has:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
Every quadratic equation has at least two roots.
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
