Advertisements
Advertisements
प्रश्न
Find the roots of the following quadratic equation by the factorisation method:
`2/5x^2 - x - 3/5 = 0`
Advertisements
उत्तर
Given equation is `2/5x^2 - x - 3/5` = 0
On multiplying by 5 on both sides, we get
2x2 – 5x – 3 = 0
⇒ 2x2 – (6x – x) – 3 = 0 ....[By splitting middle term]
⇒ 2x2 – 6x + x – 3 = 0
⇒ 2x(x – 3) + 1(x – 3) = 0
⇒ (x – 3)(2x + 1) = 0
Now, x – 3 = 0
⇒ x = 3
And 2x + 1 = 0
⇒ x = `-1/2`
Hence, the roots of the equation 2x2 – 5x – 3 = 0 are `- 1/2` and 3.
APPEARS IN
संबंधित प्रश्न
Solve for x :
`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Solve each of the following equations by factorization:
`x+1/x=2.5`
Solve the following quadratic equations by factorization:
(x + 1) (2x + 8) = (x+7) (x+3)
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
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.
Solve the following equation: 4x2 - 13x - 12 = 0
Solve the following equation: c
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
In each of the following, determine whether the given values are solution of the given equation or not:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.
The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
