Advertisements
Advertisements
प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Advertisements
उत्तर
The given quadric equation is 4x2 - 3kx + 1 = 0, and roots are real and equal
Then find the value of k.
Here, a = 4, b = -3k and c = 1
As we know that D = b2 - 4ac
Putting the value of a = 4, b = -3k and c = 1
= (-3k)2 - 4 x (4) x (1)
= 9k2 - 16
The given equation will have real and equal roots, if D = 0
Thus,
9k2 - 16 = 0
9k2 = 16
k2 = 16/9
`k=sqrt(16/9)`
`k=+-4/3`
Therefore, the value of `k=+-4/3` .
APPEARS IN
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 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.
Solve the following quadratic equation using formula method only :
16x2 = 24x + 1
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
ax2 + (4a2 - 3b)x - 12 ab = 0
Find the value of k for which the following equation has equal roots:
(k − 12)x2 + 2(k − 12)x + 2 = 0.
Solve the following by reducing them to quadratic equations:
z4 - 10z2 + 9 = 0.
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
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
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
Every quadratic equation has exactly one root.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
