Advertisements
Advertisements
Question
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Options
8
-8
4
-4
Advertisements
Solution
Let `alpha and beta `be the roots of quadratic equation `4x^2 - 2x + (λ - 4) = 0` in such a way that `alpha = 1/beta`
Here, a = 4,b = -2 and , c= (λ - 4)
Then , according to question sum of the roots
`alpha + beta = (-b)/a`
`1/beta + beta = (-(-2))/4`
`(1+beta^2) = 1/2`
`2 + 2beta^2 = beta`
`2beta^2 - beta + 2 = 0`
And the product of the roots
`alpha . beta = c/a`
`1/beta xx beta = (λ - 4)/4`
`1 = (λ -4)/4`
`λ - 4 = 4`
`λ = 4 + 4`
`= 8`
Therefore, value of `λ = 8`.
APPEARS IN
RELATED QUESTIONS
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
Solve the following quadratic equations by factorization:
(x + 1) (2x + 8) = (x+7) (x+3)
Find two consecutive multiples of 3 whose product is 648.
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
Find the values of k for which the quadratic equation
\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
If ax2 + bx + c = 0 has equal roots, then c =
The number of quadratic equations having real roots and which do not change by squaring their roots is
If one of the equation x2 + ax + 3 = 0 is 1, then its other root is
Solve the following equation:
(2x+3) (3x-7) = 0
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Find two consecutive integers such that the sum of their squares is 61
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
