Advertisements
Advertisements
प्रश्न
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
उत्तर
For the given equation x2 + 4kx + (k2 – k + 2) = 0
a = 1, b = 4k and c = k2 - k +1
Since the roots are equal,
b2 - 4ac = 0
`=> (4k)^2 - 4xx1xx(k^2 - k + 2) = 0`
`=> 16k^2 - 4k^2 + 4k - `8 = 0`
`=> 12k^2 + 4k - 8 = 0`
`=> 3k^2 + k - 2 = 0`
`=> 3k^2 + 3k - 2k - 2 = 0`
`=> 3k(k+1) - 2(k+1) = 0`
`=> (k+1) (3k - 2) = 0`
`=> k + 1 = 0 or 3k - 2 = 0`
`=> k = -1 or k = 2/3`
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Solve the following quadratic equation using formula method only
5x2 - 19x + 17 = 0
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Every quadratic equation has at least one real root.
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Solve the equation: 3x2 – 8x – 1 = 0 for x.
