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)
पर्याय
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
In the following determine the set of values of k for which the given quadratic equation has real roots:
kx2 + 6x + 1 = 0
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
α and β are the roots of 4x2 + 3x + 7 = 0, then the value of `1/α + 1/β` is:
(x2 + 1)2 – x2 = 0 has ______.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
2x2 + x – 1 = 0
Every quadratic equation has exactly one root.
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
Let α and β be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = αn + βn, n = 1, 2, 3, ....., then ______.
