Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
उत्तर
The given equation is k2x2 - 2(2k - 1)x + 4 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = k2, b = -2(2k - 1) and c = 4
therefore, the discriminant
D = b2 - 4ac
= (-2(2k - 1))2 - 4 x (k2) x (4)
= 4(2k - 1)2 - 16k2
= 4(4k2 + 1 - 4k) - 16k2
= 16k2 + 4 - 16k - 16k2
= 4 - 16k
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 4 - 16k = 0
⇒ -16k = -4
`rARrk=(-4)/-16`
⇒ k = 1/4
Hence, the value of K = 1/4
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + 3x + k = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 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.
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
