Advertisements
Advertisements
Question
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Advertisements
Solution
3x2 + 2x - 1 = 0
Here, a = 3, b = 2 and c = -1
D = b2 - 4ac
= 4 - 4 x 3 x (-1)
⇒ D = 4 + 12
= 16 > 0.
RELATED QUESTIONS
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
9x2 - 24x + k = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
(x2 + 1)2 – x2 = 0 has:
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
