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
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Find the value of p for which the quadratic equation (2p + 1)x2 − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
If the roots of the equation (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
Find the sum of the roots of the equation x2 – 8x + 2 = 0
