Advertisements
Advertisements
Question
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solution 1
`sqrt2x^2 + 7x + 5sqrt2`
= `sqrt2 x^2 + 5x + 2x + 5sqrt2`
= `x (sqrt2x + 5) + sqrt2(sqrt2x + 5)`
= `(sqrt2x + 5)(x + sqrt2) = 0`
Roots of this equation are the values for which `(sqrt2x + 5)(x + sqrt2) = 0`
`:.sqrt2x + 5 = 0 orx + sqrt2 = 0`
⇒ `x = (-5)/sqrt2 or x = -sqrt2`
Solution 2
We write 7x = 5x + 2x as `sqrt2x^2 xx 5sqrt2 = 10x^2 = 5x xx 2x`
`:.sqrt2x^2 + 7x + 5sqrt2 = 0`
`=>sqrt2x^2+ 5x + 2x + 5sqrt2 = 0`
`=> x(sqrt2x + 5) + sqrt2(sqrt2x + 5) = 0`
`=> (sqrt2x + 5)(x + sqrt2) = 0`
`=> x + sqrt2 = 0` or `sqrt2x + 5 = 0`
`=> x = -sqrt2 or x = - 5/sqrt2 = -(5sqrt2)/2`
Hence, the roots of the given equation are `-sqrt2 and-(5sqrt2)/2`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Find two numbers whose sum is 27 and product is 182.
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
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.
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
The sum of a natural number and its square is 156. Find the number.
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
Solve the following quadratic equation by factorisation.
3x2 - 2√6x + 2 = 0
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Find the factors of the Polynomial 3x2 - 2x - 1.
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
Solve the following equation by factorization
`3x - (8)/x `= 2
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
If x4 – 5x2 + 4 = 0; the values of x are ______.
