Advertisements
Advertisements
प्रश्न
Find the values of k for the following quadratic equation, so that they have two equal roots.
kx (x - 2) + 6 = 0
Advertisements
उत्तर
kx(x - 2) + 6 = 0
or kx2 - 2kx + 6 = 0
Comparing this equation with ax2 + bx + c = 0, we get
a = k, b = - 2k and c = 6
Discriminant = b2 - 4ac
= (-2k)2 - 4 (k) (6)
= 4k2 - 24k
k2 - 6k = 0
k (k - 6) = 0
For equal roots,
b2 - 4ac = 0
4k2 - 24k = 0
4k (k - 6) = 0
Either 4k = 0 or k = 6 = 0
k = 0 or k = 6
However, if k = 0, then the equation will not have the terms 'x2' and 'x'.
Therefore, if this equation has two equal roots, k should be 6 only.
APPEARS IN
संबंधित प्रश्न
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Form the quadratic equation if its roots are –3 and 4.
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:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Solve the following quadratic equation using formula method only
25x2 + 30x + 7 = 0
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
ax2 + (4a2 - 3b)x - 12 ab = 0
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
The roots of the equation 7x2 + x – 1 = 0 are:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is ______.
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
If 3 is a root of the quadratic equation x2 – px + 3 = 0 then p is equal to ______.
Equation 2x2 – 3x + 1 = 0 has ______.
