Advertisements
Advertisements
प्रश्न
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
उत्तर
Given quadratic equation is 3x2 – 5x – 2k = 0
For real and equal roots D = 0; i.e., b2 – 4ac = 0
On comparing the given equation with ax2 + bx + c = 0, we get
a = 3, b = –5 and c = –2k
∴ b2 – 4ac = 0
⇒ (–5)2 – 4(3)(–2k) = 0
⇒ 25 + 24k = 0
⇒ k = `- 25/24`
संबंधित प्रश्न
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
If the roots of the equation (a2 + b2)x2 − 2 (ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b=c/d`.
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Solve the following quadratic equation using formula method only
x2 - 4x - 1 = 0
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Find if x = – 1 is a root of the equation 2x² – 3x + 1 = 0.
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
