Advertisements
Advertisements
Question
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Solution
The given quadric equation is 4x2 - 3kx + 1 = 0, and roots are real
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 roots, if D ≥ 0
⇒ 9k2 - 16 ≥ 0
⇒ 9k2 ≥ 16
⇒ k2 ≥ 16/9
`rArrk>=sqrt(16/9)` or `k<=-sqrt(16/9)`
⇒ k ≥ 4/3 Or k ≤ -4/3
APPEARS IN
RELATED QUESTIONS
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(k + 1)x + (k + 4) = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
