Advertisements
Advertisements
प्रश्न
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Advertisements
उत्तर
The given equation is `"x"^2 + 4"x" + "k" = 0`
For real roots, D ≥ 0
⇒ `"b"^2 – 4"ac" ≥ 0`
⇒ `4^2 – 4(1) ("k") ≥ 0`
⇒ 4 – k ≥ 0
⇒ `"k" ≤ 4`
For `"k" ≤ 4`, the given equation `"x"^2 + 4"x" + "k"` = 0 has real roots.
संबंधित प्रश्न
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
