Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Using quadratic formula find the value of x.
abx2 + (b2 – ac)x – bc = 0
उत्तर
We have been given
abx2 + (b2 – ac)x – bc = 0
abx2 + b2x – acx – bc = 0
bx(ax + b) – c(ax + b) = 0
(ax + b)(bx – c) = 0
Therefore,
ax + b = 0
ax = – b
`x = (-b)/a`
or
bx – c = 0
bx = c
`x = c/b`
Hence, `x=(-b)/a` or `x = c/b`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Solve the following quadratic equation by factorization:
`sqrt(6)x^2 - 4x - 2sqrt(6) = 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 equation for x:
x2 − 4ax − b2 + 4a2 = 0
Factorise : m2 + 5m + 6.
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
In each of the following determine whether the given values are solutions of the equation or not.
x2 + x + 1 = 0; x = 1, x = -1.
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)`
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.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
