Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 4sqrt(3)x + 4` = 0
उत्तर
`3x^2 - 4sqrt(3)x + 4` = 0
Here a = 3, b = `-4sqrt(3)`, c = 4
∴ D = b2 - 4ac
= `(-4sqrt(3))^2 - 4 xx 3 xx 4`
= 48 - 48
= 0
∵ D = 0
∴ Roots are real and equal.
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Choose the correct answer from the given four options :
If the equation {k + 1)x² – 2(k – 1)x + 1 = 0 has equal roots, then the values of k are
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
