Advertisements
Advertisements
प्रश्न
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
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
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(3k+1)x2 + 2(k + 1)x + k = 0
Find the values of k for which the roots are real and equal in each of the following equation:
2x2 + kx + 3 = 0
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Which of the following equations has 2 as a root?
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.