Advertisements
Advertisements
Question
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`
Advertisements
Solution
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3)` = 0.
Here, `a = 2sqrt(3), b = -2sqrt(2) and c = -sqrt(3)`
D = b2 - 4ac
⇒ D - 8 - 4 x 2`sqrt(3) xx- sqrt(3)`
⇒ D = 8 + 24
= 32 > 0
The given equation has real roots.
RELATED QUESTIONS
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 values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + kx + 1 = -4x2 - x
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − 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).
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’
