Advertisements
Advertisements
Question
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
Advertisements
Solution
Given that `(1 + sqrt2)` is a root of the quadratic equation with rational coefficients.
Then find the other root.
As we know that if `(1 + sqrt2)`is a root of the quadratic equation with rational coefficients then other roots be `(1 - sqrt2)`.
Hence, the require root of the quadratic equation be `(1 - sqrt2)`.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Solve the following quadratic equations by factorization:
(x + 1) (2x + 8) = (x+7) (x+3)
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
The sum of a number and its reciprocal is `2 9/40`. Find the number.
Solve (x2 + 3x)2 - (x2 + 3x) -6 = 0.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
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^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Solve the following equation by factorization
`3x - (8)/x `= 2
If x4 – 5x2 + 4 = 0; the values of x are ______.
