Advertisements
Advertisements
प्रश्न
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Advertisements
उत्तर
x = 2 is a root of given equation
substitute x = 2 in L.H.S.
L.H.S. = 3(2)2 - 2k x 2 + 2m = 0
12 - 4k + 2m = 0
4k - 2m = 12 ...(i)
Similarly when x = 2 is root of given equation
Substitute x = 3 in L.H.S.
L.H.S. = 3(3)2 - 2k x 3 + 2m = 0
27 - 6k + 2m = 0
6k - 2m = 27 ...(ii)
On solving equation (i) and (ii), we get
k = `(15)/(2)` and m = 9.
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Determine the nature of the roots of the following quadratic equation:
(b + c)x2 – (a + b + c)x + a = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2 - 2sqrt(ac)x + b = 0` are simultaneously real, then prove that b2 = ac.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
`10x -(1)/x` = 3
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Solve for x: 9x2 – 6px + (p2 – q2) = 0
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
