Advertisements
Advertisements
Question
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
Options
1
2
3
4
Advertisements
Solution
x = 1 is the common roots given quadric equation are , ax2 + ax + 2 = 0 and x2 + x + b = 0
Then find the value of ab.
Here, ax2 + ax + 2 = 0 ….. (1)
x2 + x + b = 0….. (2)
Putting the value of x = 1in equation (2) we get
`1^2 + 1+b = 0`
`2 + b = 0`
` b = -2`
Now, putting the value of x= 1 in equation (1) we get
`a + a + 2 = 0`
` 2a + 2 = 0`
`a = (-2)/2`
`=-1`
Then, `ab = (-1) xx (-2)`
= 2
APPEARS IN
RELATED QUESTIONS
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
Solve the following quadratic equations by factorization:
ax2 + (4a2 − 3b)x − 12ab = 0
Divide 29 into two parts so that the sum of the squares of the parts is 425.
Find two consecutive multiples of 3 whose product is 648.
Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Find the values of x if p + 1 =0 and x2 + px – 6 = 0
If the product of two consecutive even integers is 224, find the integers.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Two pipes running together can fill a tank in `11(1)/(9)` minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would/fill the tank.
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:
`21x^2 - 2x + 1/21 = 0`
