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:
2x2 – 6x + 3 = 0
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Determine the nature of the roots of the following quadratic equation:
(x – 2a)(x – 2b) = 4ab
Form the quadratic equation whose roots are:
`sqrt(3) and 3sqrt(3)`
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Choose the correct answer from the given four options :
If the equation 2x² – 6x + p = 0 has real and different roots, then the values of p are given by
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
(x2 + 1)2 – x2 = 0 has ______.
The roots of quadratic equation x2 – 1 = 0 are ______.
When the discriminant satisfies \( D > 0 \), what is the nature of the roots of the quadratic equation?
