Advertisements
Advertisements
Question
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
Advertisements
Solution
(k – 4) x2 + 2(k – 4) x + 4 = 0
Here a = k - 4, b = 2(k - 4), c = 4
D = b2 - 4ac
= [2(k - 4)]2 - 4 x (k - 4) x 4
= 4(k2 + 16 - 8k) - 16(k - 4)
= 4(k2 - 8k + 16) - 16(k - 4)
= 4[k2 - 8k + 16 - 4k + 16]
= 4(k2 - 12k + 32)
∵ Roots are equal
∴ D = 0
⇒ 4(k2 - 12k + 32) = 0
⇒ k2 - 12k + 32 = 0
⇒ k2 - 8k - 4k + 32 = 0
⇒ k(k - 8) -4(k - 8) = 0
⇒ (k - 8)(k - 4) = 0
Either k - 8 = 0,
then k = 4
or
k - 4 = 0,
then k = 4
But k - 4 ≠ 0
k ≠ 4
k = 8.
APPEARS IN
RELATED QUESTIONS
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Determine the nature of the roots of the following quadratic equation :
4x2 - 8x + 5 = 0
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
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 ______.
