Advertisements
Advertisements
Question
If one of the equation x2 + ax + 3 = 0 is 1, then its other root is
Options
3
-3
2
1
Advertisements
Solution
Let `alpha and beta`be the roots of quadratic equation`x^2 + ax + 3 =0`in such a way that `alpha = 1`
Here, a = 1, b = a and ,c = 3
Then , according to question sum of the roots
`alpha + beta = (-b)/ a`
`1 + beta = (-a)/1`
`beta = -a -1`
And the product of the roots
`alpha . beta = 3/1`
`1 xx beta = 3`
`beta = 3`
Therefore, value of other root be `beta = 3`.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
The sum of a natural number and its square is 156. Find the number.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Solve the following equation: 25x (x + 1) = -4
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
Solve the following quadratic equation using formula method only
6x2 + 7x - 10 = 0
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
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 following quadratic equation by factorisation method:
`(x + 3)/(x - 2) - (1 - x)/x = (17)/(4)`.
Solve the following equation by factorization
x(2x + 5) = 3
Find three successive even natural numbers, the sum of whose squares is 308.
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
(x – 3) (x + 5) = 0 gives x equal to ______.
