Advertisements
Advertisements
प्रश्न
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Advertisements
उत्तर
The given quadric equation is x2 + ax − 1 = 0
Then find the value of a.
Here, a= 1, b = a and, c = -1
As we know that `D = b^2 - 4ac`
Putting the value of a= 1, b = a and, c = -1
` = (a)^2 - 4 xx 1 xx -1`
` = a^2 + 4`
The given equation will have real roots, if D > 0.
`a^2 + 4 >0`
⇒ `a^2 > - 4`which is true for all real values of a.
Therefore, for all real values of a, the given equation has real roots.
APPEARS IN
संबंधित प्रश्न
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?
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Solve each of the following equations by factorization:
`9/2x=5+x^2`
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Solve the following equation by factorization
x (2x + 1) = 6
If the product of two consecutive even integers is 224, find the integers.
If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.
For quadratic equation `2x + 5/x = 5` :
