Advertisements
Advertisements
Question
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
Advertisements
Solution
The given quadric equation is kx2 + 6x + 1 = 0, and roots are real and distinct.
Then find the value of k.
Here,
a = k, b = 6 and c = 1
As we know that D = b2 - 4ac
Putting the value of a = k, b = 6 and c = 1
D = (6)2 - 4 x (k) x (1)
= 36 - 4k
The given equation will have real and distinct roots, if D > 0
36 - 4k > 0
Now factorizing of the above equation
36 - 4k > 0
4k < 36
k < 36/4
k < 9
Now according to question, the value of k less than 9
Therefore, the value of k < 9.
APPEARS IN
RELATED QUESTIONS
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
If a = 1, b = 4, c = – 5, then find the value of b2 – 4ac
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
