Advertisements
Advertisements
प्रश्न
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
Advertisements
उत्तर
x² + (p – 3) x + p = 0
Here a = 1, b = p - 3, c = p
For real and equal roots
D = b2 - 4ac = 0
(p - 3)2 - 4 x 1 x p = 0
p2 - 6p + 9 - 4p = 0
p2 - 10p + 9 = 0
⇒ p2 - p - 9 (p - 1) = 0
p(p - 1) - 9 (p - 1) = 0
⇒ (p - 1) (p - 9) = 0
⇒ p = 1 or p = + 9
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
3x2 + 2x + k = 0
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
48x² – 13x -1 = 0
`10x -(1)/x` = 3
`(2)/x^2 - (5)/x + 2` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Discuss the nature of the roots of the following quadratic equations : `x^2 - (1)/(2)x + 4` = 0
The roots of quadratic equation x(x + 8) + 12 = 0 are ______.
