Advertisements
Advertisements
Question
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
Advertisements
Solution
The given quadric equation is kx2 + 2x + 1 = 0, and roots are real and distinct
Then find the value of k.
Here,
a = k, b = 2 and c = 1
As we know that D = b2 - 4ac
Putting the value of a = k, b = 2 and c = 1
D = (2)2 - 4 x (k) x (1)
= 4 - 4k
The given equation will have real and distinct roots, if D > 0
4 - 4k > 0
Now factorizing of the above equation
4 - 4k > 0
4k < 4
k < 4/4
k < 1
Now according to question, the value of k less than 1
Therefore, the value of k < 1.
APPEARS IN
RELATED QUESTIONS
Solve for x : ` 2x^2+6sqrt3x-60=0`
Determine the nature of the roots of the following quadratic equation:
`3/5x^2-2/3x+1=0`
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx - 4 = 0
Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 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)`.
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x2 + 2(k – 4) x + 4 = 0
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
