Advertisements
Advertisements
प्रश्न
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
उत्तर
3x2 – 5x – 2m = 0
Here a = 3, b = -5, c = -2m
∴ D = b2 – 4ac
= (5)2 –4 x 3 x (–2m)
= 25 + 24m
∵ Roots are real and distinct
∴ D> 0
25 + 24m > 0
24m > –25
m > `-(25)/(24)`.
APPEARS IN
संबंधित प्रश्न
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Find the value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
Solve the following quadratic equation using formula method only
`2x^2 - 2 . sqrt 6x + 3 = 0`
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Which of the following equations has two real and distinct roots?
