Advertisements
Advertisements
प्रश्न
Choose the correct answer from the given four options :
The value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are)
विकल्प
0 only
4
8
0, 8
Advertisements
उत्तर
2x² – kx + k = 0
a = 2, b = -k, c = k
∴ b2 - 4ac
= (-k)2 - 4 x 2 x 4
= k2 - 8k
∴ Roots are equal.
∴ b2 - 4ac = 0
k2 - 8k = 0
⇒ k(k - 8) = 0
Either k = 0
or
k - 8 = 0,
then k = 8
k = 0, 8.
APPEARS IN
संबंधित प्रश्न
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Determine the nature of the roots of the following quadratic equation:
`3x^2-2sqrt6x+2=0`
Determine the nature of the roots of the following quadratic equation :
x2 -5x+ 7= 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 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
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
If (1 – p) is a root of the equation x2 + px + 1 – p = 0, then roots are:
Every quadratic equations has at most two roots.
