Advertisements
Advertisements
प्रश्न
Solve for x: 9x2 – 6px + (p2 – q2) = 0
उत्तर
a = 9, b = − 6p, c = p2 − q2
D = b2 − 4ac = (− 6p)2 − 4(9)(p2 − q2) = 36q2
x = `(- b +- sqrt(D))/(2q) = (6p +- 6q)/18 = (p + q)/3` or `(p - q)/3`
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Discuss the nature of the roots of the following quadratic equations : `3x^2 - 2x + (1)/(3)` = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
If the one root of the equation 4x2 – 2x + p – 4 = 0 be the reciprocal of the other. The value of p is:
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
x2 – 3x + 4 = 0
