Advertisements
Advertisements
प्रश्न
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Advertisements
उत्तर
(4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0
Here a = (4 – k), b = 2 (k + 2), c = 8k + 1
∴ D = b2 – 4ac
= [2(k + 2)]2 – 4 x (4 – k)(8k + 1) = 0
= 4(k + 2)2 - 4(32k + 4 – 8k2 – k)
= 4(k2 + 4k + 4) –4(32k + 4 – 8k2 – k)
= 4k2 + 16k + 16 - 128k – 16 + 32k2 + 4k
= 36k2 – 108k
= 36k(k – 3)
∵ Roots are equal
∴ D = 0
⇒ 36k(k – 3) = 0
⇒ k(k – 3) = 0
Either k = 0
or
k – 3 = 0,
then k= 3
k = 0, 3.
APPEARS IN
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Prove that both the roots of the equation (x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 are real but they are equal only when a = b = c.
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.
Which of the following equations has imaginary roots?
