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
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
Solve the following quadratic equations by factorization:
`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5
Two numbers differ by 3 and their product is 504. Find the number
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
`x^2-4x+1=0`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
If ax2 + bx + c = 0 has equal roots, then c =
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
6p2+ 11p – 10 = 0
Solve the following equation by factorization
`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
If `x + 1/x = 2.5`, the value of x is ______.
