Advertisements
Advertisements
प्रश्न
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Advertisements
उत्तर
The given quadratic equation is:
9x2 + 3kx + 4 = 0
Here, a = 9, b = 3k and c = 4.
This equation has real roots if
Calculate the discriminant D of the given equation as follows:
D = b2 − 4ac
⇒ (3k)2 − (4 x 9 x 4)
⇒ 9k2 − 144
Since the given equation has equal roots, the discriminant must be equal to zero.
D = 0
⇒ 9k2 − 144 = 0
⇒ 9k2 = 144
⇒ k2 = `(144)/(9)`
⇒ k = `sqrt((144)/(9))`
⇒ k = ± 4
Hence, the required value is k = 4 and k = −4.
संबंधित प्रश्न
Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2? If so, find its length and breadth.
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Find the value of the discriminant in the following quadratic equation :
`4 sqrt 3 "x"^2 + 5"x" - 2 sqrt 3 = 0`
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
48x² – 13x -1 = 0
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
If a = 1, b = 4, c = –5, then find the value of b2 – 4ac.
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
