Advertisements
Advertisements
प्रश्न
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
पर्याय
x2 + 4 = 0
x2 − 4 = 0
4x2 − 1 = 0
x2 − 2 = 0
Advertisements
उत्तर
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is x2 − 4 = 0.
Explanation:
Let α and β be the roots of quadratic equation in such a way that a = 2
Then, according to question sum of the roots
α + β = 0
2 + β = 0
β = – 2
And the product of the roots
α . β = 2 × (– 2)
= – 4
As we know that the quadratic equation
x2 – (α + β) x + αβ = 0
Putting the value of α and β in above
Therefore, the require equation be
x2 − 0 × x + (− 4) = 0
x2 − 4 = 0
APPEARS IN
संबंधित प्रश्न
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
The sum of a natural number and its square is 156. Find the number.
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equation by factorisation.
x2 + x – 20 = 0
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
Solve (x2 + 3x)2 - (x2 + 3x) -6 = 0.
Solve the following equation by factorization
3(x – 2)2 = 147
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
