Advertisements
Advertisements
Question
If one of the equation ax2 + bx + c = 0 is three times times the other, then b2 : ac =
Options
3 : 1
3 : 16
16 : 3
16 : 1
Advertisements
Solution
Let `alpha and beta`be the roots of quadratic equation`ax^2 + bx + c = 0` in such a way that `alpha = 3beta`
Here, a = a, b = b and , c = c
Then,
according to question sum of the roots
`alpha + beta = (-b)/a`
`3 beta + beta = (-b)/a`
`4beta = (-b)/a`
`alpha = (-b)/(4a)`….. (1)
And the product of the roots
`alpha . beta = c/a`
`3beta xx beta = c / a`
`3beta^2 = c/a`
`beta^2 = c /3a`….. (2)
Putting the value of `beta = (-b)/(4a)` in equation (2)
`(-b)/(4a)^2 = c /(3a)`
`(b^2)/(16a^2) = c/3a`
`b^2 = c/(3a) xx 16a^2`
`b^2 = (16ac)/3`
`b^2 / (ac) = 16/3`
`b^2 : ac = 16 :3`
APPEARS IN
RELATED QUESTIONS
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
The sum of two numbers is 48 and their product is 432. Find the numbers?
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Solve the following : `("x" - 1/2)^2 = 4`
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve equation using factorisation method:
x2 – (a + b)x + ab = 0
Solve the following quadratic equation by factorisation method:
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`.
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Solve the following equation by factorization
3x2 – 5x – 12 = 0
Find two consecutive odd integers such that the sum of their squares is 394.
Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
