Problem 1 :
For what value of K the roots of equation 2x^{2} + 5x + k = 0 will be rational and equal.
For what value of K the roots of the given equations are equal.
Problem 2 :
x^{2} + 3(k + 1)x + 4k + 5 = 0
Problem 3 :
x^{2} + 2(k – 2)x – 8k = 0
Problem 4 :
(3k + 6)x^{2} + 6x + k = 0
Problem 5 :
(k + 2)x^{2} – 2kx + k – 1 = 0
Problem 6 :
For what value of k the equation (4–k) x^{2} + 2(k+2) x + 8k + 1 = 0 will be a perfect square.
(Hint : The equation will be perfect square if Disc. b^{2} – 4ac = 0 )
1) k = 25/8
2) So, the value of k are 1 and -11/9.
3) So, the value of k is -2.
4) So, the values of k are -3 and 1.
5) k = 2
6) So, the value of k are 0 and 3.
Problem 1 :
Find all the values of a such that
ax^{2} + 3x + 5 = 0
has two real roots.
Problem 2 :
Find all values of a such that ax^{2} + 48x + 64 = 0 has one real root (a double root)
Problem 3 :
Find all the values of a such that
ax^{2} + 3x - 6 = 0
has two imaginary roots.
Problem 4 :
Find all the values of such that
2x^{2} - 6x + c = 0
has two imaginary roots.
Problem 5 :
Find all values of c such that -4x^{2} + 8x + c = 0 has two real roots.
1) a < 9/20
2) a = 9
3) a < -3/8
4) a > 9/2
5) c > -4
Feb 25, 24 07:44 AM
Feb 24, 24 11:07 PM
Feb 24, 24 08:49 PM