Advertisements
Advertisements
प्रश्न
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
Advertisements
उत्तर
2x2 + x – 6
= 2x2 + 4x - 3x - 6
= 2x(x + 2) - 3(x + 2)
= (x + 2)(2x - 3)
Roots of this equation are the values for which (x + 2)(2x - 3) = 0
⇒ x = -2 or x = `3/2`
APPEARS IN
संबंधित प्रश्न
Find two consecutive positive integers, sum of whose squares is 365.
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Two natural number differ by 3 and their product is 504. Find the numbers.
Find the tow consecutive positive odd integer whose product s 483.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
Solve the following quadratic equation by factorisation method:
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`.
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
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.
