Advertisements
Advertisements
प्रश्न
`8x^2-14x-15=0`
Advertisements
उत्तर
`8x^2-14x-15=0`
⇒`16x^2-28x-30=0`
⇒`16x^2-28x=30`
⇒`(4x)^2-2xx4x xx7/2+(7/2)^2=30+(7/2)^2`
⇒`(4x-7/2)^2=30+49/4=169/4=(13/2)^2`
⇒`4x-7/2=+-13/2`
⇒`4x=7/2=13/2 or 4x-7/2=13/2`
⇒`4x=13/2+7/2=20/2=10 or 4x=-13/2+7/2=6/2=-3`
⇒`x=5/2 or x=-3/4`
Hence, `5/2 and -3/4` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve equation using factorisation method:
(2x – 3)2 = 49
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
Find the roots of the following quadratic equation by the factorisation method:
`2/5x^2 - x - 3/5 = 0`
(x – 3) (x + 5) = 0 gives x equal to ______.
