Advertisements
Advertisements
Question
Find the values of k for which the roots are real and equal in each of the following equation:
k2x2 - 2(2k - 1)x + 4 = 0
Advertisements
Solution
The given equation is k2x2 - 2(2k - 1)x + 4 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = k2, b = -2(2k - 1) and c = 4
therefore, the discriminant
D = b2 - 4ac
= (-2(2k - 1))2 - 4 x (k2) x (4)
= 4(2k - 1)2 - 16k2
= 4(4k2 + 1 - 4k) - 16k2
= 16k2 + 4 - 16k - 16k2
= 4 - 16k
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 4 - 16k = 0
⇒ -16k = -4
`rARrk=(-4)/-16`
⇒ k = 1/4
Hence, the value of K = 1/4
APPEARS IN
RELATED QUESTIONS
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
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
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Solve the following quadratic equation using formula method only
`3"x"^2 + 2 sqrt 5x - 5 = 0 `
(3x - 5)(2x + 7) = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 + 5x + 15 = 0.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: (3m + 1)x2 + 2(m + 1)x + m = 0
Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0
Choose the correct alternative answer for the following sub questions and write the correct alphabet.
If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X2 + 2X + k = 0
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
Which of the following equations has imaginary roots?
