Advertisements
Advertisements
प्रश्न
`7x^2+3x-4=0`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
The sum of a natural number and its square is 156. Find the number.
The sum of two natural number is 28 and their product is 192. Find the numbers.
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Determine whether the values given against the quadratic equation are the roots of the equation.
2m2 – 5m = 0, m = 2, `5/2`
If the equation x2 + 4x + k = 0 has real and distinct roots, then
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
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 quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Solve the following equation by factorisation :
x2 + 6x – 16 = 0
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
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.
