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
Is it possible to design a rectangular park of perimeter 80 and area 400 m2? If so find its length and breadth.
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0
Complete the following activity to find the value of discriminant for quadratic equation 4x2 – 5x + 3 = 0.
Activity: 4x2 – 5x + 3 = 0
a = 4, b = ______, c = 3
b2 – 4ac = (–5)2 – (______) × 4 × 3
= ( ______ ) – 48
b2 – 4ac = ______
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
