Advertisements
Advertisements
Question
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Solution
The given quadric equation is `kx^2-2sqrt5x+4=0`, and roots are real and equal
Then find the value of k.
Here, a = k, `b=-2sqrt5`, and c = 4
As we know that D = b2 - 4ac
Putting the value of a = k, `b=-2sqrt5`, and c = 4
`=(-2sqrt5)^2-4xxkxx4`
= 20 - 16k
The given equation will have real and equal roots, if D = 0
Thus,
20 - 16k = 0
16k = 20
k = 20/16
k = 5/4
Therefore, the value of k = 5/4.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation for x :
9x2 − 6b2x − (a4 − b4) = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
Solve the following quadratic equation using formula method only
`3"x"^2 - 5"x" + 25/12 = 0 `
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
(x2 + 1)2 – x2 = 0 has ______.
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
–3x2 + 5x + 12 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
