Advertisements
Advertisements
प्रश्न
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
उत्तर
x2 – 3x – 10
= x2 - 5x + 2x - 10
= x(x - 5) + 2(x - 5)
= (x - 5)(x + 2)
Roots of this equation are the values for which (x - 5)(x + 2) = 0
⇒ x = 5 or x = -2
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
The sum of two numbers is 48 and their product is 432. Find the numbers?
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
The sum of natural number and its reciprocal is `65/8` Find the number
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
If the equation x2 − bx + 1 = 0 does not possess real roots, then
Solve the following equation: 2x2 - 3x - 9=0
Solve equation using factorisation method:
`2x^2 - 1/2x = 0`
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.
A boat can cover 10 km up the stream and 5 km down the stream in 6 hours. If the speed of the stream is 1.5 km/hr. find the speed of the boat in still water.
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
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.
At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.
