Advertisements
Advertisements
प्रश्न
If the equation ax2 + 2x + a = 0 has two distinct roots, if
विकल्प
a = ±1
a = 0
a = 0, 1
a = −1, 0
Advertisements
उत्तर
a = ±1
Explanation:
If the roots of given equation are distinct then
d = b2 – 4ac = 0
⇒ d = b2 – 4ac = 0
⇒ 22 – 4(a) (a) = 0
⇒ 4 – 4a2 = 0
⇒ 4a2 = 4
⇒ a2 = 1
⇒ a = ±1
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
Solve the following quadratic equations by factorization:
48x2 − 13x − 1 = 0
The sum of a numbers and its positive square root is 6/25. Find the numbers.
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Solve the following quadratic equations by factorization:
`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`
The sum of a natural number and its square is 156. Find the number.
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Solve the following quadratic equation by factorisation.
x2 + x – 20 = 0
The number of quadratic equations having real roots and which do not change by squaring their roots is
Solve the following equation:
(2x+3) (3x-7) = 0
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Solve the following equation by factorization
`3x - (8)/x `= 2
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
If the discriminant of the quadratic equation 3x2 - 2x + c = 0 is 16, then the value of c is ______.
