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: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
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:
3x2 + 2x + k = 0
If x = −2 is a root of the equation 3x2 + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x2 + k(4x + k − 1) + p = 0 are equal.
Solve the following quadratic equation using formula method only
4 - 11 x = 3x2
(3x - 5)(2x + 7) = 0
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
A quadratic equation with integral coefficient has integral roots. Justify your answer.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
Every quadratic equations has at most two roots.
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
