Advertisements
Advertisements
Question
Solve: x(x + 1) (x + 3) (x + 4) = 180.
Solution
Given equation
x(x + 1) (x + 3) (x + 4) = 180
⇒ [(x + 0) (x + 4)] [(x + 1) (x + 3)] = 180
⇒ (x2 + 4x) (x2 + 4x + 3) - 180 = 0
Put x2 + 4x = y,
then it becomes y(y + 3) - 180 = 0
⇒ y2 + 3y - 180 = 0
⇒ y2 + 15y - 12y - 180 = 0
⇒ y(y + 15) - 12(y + 15) = 0
⇒ (y + 15) (y - 12) = 0
⇒ y = 15 = 0 or y = 12
But x2 + 4x = y
Then x2 + 4x = -15
x2 + 4x + 15 = 0
or
x2 + 4x = 12
⇒ x2 + 4x - 12 = 0
x2 + ax + 15 = 0 gives x = `(-4 ± sqrt((4)^2 - 4 xx 15))/(2)`
= `(-4 ± sqrt(16 - 60))/(2)`
= `(-4 ± sqrt(-34))/(2)`
∴ Roots of the equation are imaginary hence not acceptable.
or
x2 + 4x - 12 = 0
⇒ x2 + 6x - 2x - 12 = 0
⇒ x (x + 6) -2 (x + 6) = 0
⇒ (x + 6) (x - 2) = 0
⇒ x + 6 = 0 or x - 2 = 0
⇒ x = -6 or x = 2.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also find the solution of the equation:
3x2 + 12x + (m + 7) = 0
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
