Advertisements
Advertisements
Question
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Advertisements
Solution
`px^2 - 4x + 3 = 0`
Here a = p, b = -4 and c = 3
Given equation has equal roots then D = 0
`=> b^2 - 4ac = 0`
`=> [-4]^2 - 4(p)(3) = 0`
`=> 16 - 12p = 0`
`=> -12p = -16`
`=> p = (-16)/(-12) = 4/3`
RELATED QUESTIONS
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Find the two consecutive positive even integers whose product is 288.
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
If p and q are the roots of the equation x2 – px + q = 0, then ______.
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
