Advertisements
Advertisements
Question
`7x^2+3x-4=0`
Advertisements
Solution
`7x^2+3x-4=0`
⇒`49x^2+21x-28=0` (Multiplying both sides by 7)
⇒`49x^2+21x=28`
⇒`(7x)^2+xx7x xx3/2+(3/2)^2=28+(3/2)^2` [Adding (3/2)^2 on both sides]
⇒`(7x+3/2)^2=28+9/4=121/4=(11/2)^2`
⇒`7x+3/2=+-11/2` (Taking square root on both sides)
⇒`7x+3/2=11/2 or 7x+3/2=-11/2`
⇒`7x=11/2-3/2=8/2=4 or 7x=11/2-3/2=-14/2=-7`
⇒`x=4/7 or x=-1`
Hence, `4/7 and -1` are the roots of the given equation.
APPEARS IN
RELATED QUESTIONS
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
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
`8x^2-14x-15=0`
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Solve the following equation by factorization
x2 – 3x – 10 = 0
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
3(x – 2)2 = 147
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
Solve the following equation by factorization
x2– 4x – 12 = 0,when x∈N
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
Find the roots of the quadratic equation x2 – x – 2 = 0.
