Advertisements
Advertisements
Question
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
Advertisements
Solution
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
RELATED QUESTIONS
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Write the value of k for which the quadratic equation x2 – kx + 4 = 0 has equal roots.
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
Solve the following quadratic equation:
x2 + 4x – 8 = 0
Give your Solution correct to one decimal place.
(Use mathematical tables if necessary.)
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
Which of the following equations has imaginary roots?
