Advertisements
Advertisements
प्रश्न
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
विकल्प
−2
2
\[- \frac{1}{2}\]
\[\frac{1}{2}\]
Advertisements
उत्तर
Equation is x2 − x = λ (2x − 1)
x2 – x – λ (2x – 1) = 0
x2 – (2λ + 1)x + λ = 0
Here a = 1, b = – (2λ + 1), c = λ
Sum of the roots = `– b/a`
⇒ – (– (2λ + 1)) = 0
⇒ λ = `– 1/2`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
Solve the following quadratic equations by factorization:
25x(x + 1) = -4
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
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 girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
Solve 2x2 – 9x + 10 =0; when x ∈ Q
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
The number of quadratic equations having real roots and which do not change by squaring their roots is
Solve the following equation: 4x2 + 16x = 0
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
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.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + 6x + 5 = 0; x = -1, x = -5
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
If the product of two consecutive even integers is 224, find the integers.
Find three successive even natural numbers, the sum of whose squares is 308.
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
