Advertisements
Advertisements
प्रश्न
If one of the equation ax2 + bx + c = 0 is three times times the other, then b2 : ac =
विकल्प
3 : 1
3 : 16
16 : 3
16 : 1
Advertisements
उत्तर
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
संबंधित प्रश्न
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Solve the following quadratic equations by factorization:
`1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6`
The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.
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 product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Solve each of the following equations by factorization:
`9/2x=5+x^2`
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
