# USING DISCRIMINANT FIND THE MISSING COEFFICIENT WORKSHEET

Problem 1 :

For what value of K the roots of equation 2x2 + 5x + k = 0 will be rational and equal.

Solution

For what value of K the roots of the given equations are equal.

Problem 2 :

x2 + 3(k + 1)x + 4k + 5 = 0

Solution

Problem 3 :

x2 + 2(k – 2)x – 8k = 0

Solution

Problem 4 :

(3k + 6)x2 + 6x + k = 0

Solution

Problem 5 :

(k + 2)x2 – 2kx + k – 1 = 0

Solution

Problem 6 :

For what value of k the equation (4–k) x2 + 2(k+2) x + 8k + 1 = 0 will be a perfect square.

(Hint : The equation will be perfect square if Disc. b2 – 4ac = 0 )

Solution

## Answer Key

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

ax2 + 3x + 5 = 0

has two real roots.

Solution

Problem 2 :

Find all values of a such that ax2 + 48x + 64 = 0 has one real root (a double root)

Solution

Problem 3 :

Find all the values of a such that

ax2 + 3x - 6 = 0

has two imaginary roots.

Solution

Problem 4 :

Find all the values of such that

2x2 - 6x + c = 0

has two imaginary roots.

Solution

Problem 5 :

Find all values of c such that -4x2 + 8x + c = 0 has two real roots.

Solution

1) a < 9/20

2)  a = 9

3)  a < -3/8

4)  a > 9/2

5)  c > -4

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