Advertisements
Advertisements
प्रश्न
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Advertisements
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 nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Every quadratic equation has exactly one root.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 1)(x – 2) + x = 0
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
