Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
Advertisements
उत्तर
The given equation is x2 - 4kx + k = 0
The given equation is in the form of ax2 + bx + c = 0
where a = 1, b = -4k and c = k
Therefore, the discriminant
D = b2 - 4ac
= (-4k)2 - 4 x (1) x (k)
= 16k2 - 4k
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 16k2 - 4k = 0
⇒ 4k(4k - 1) = 0
⇒ 4k = 0
⇒ k = 0
Or
⇒ 4k - 1 = 0
⇒ 4k = 1
⇒ k = 1/4
Hence, the value of k = 0, 1/4
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the quadratic equation (3k + 1) x2 + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.
Form the quadratic equation if its roots are –3 and 4.
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
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
2x2 -3x+ 4= 0
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
