NATURE OF ROOTS OF QUADRATIC EQUATION WORKSHEET

Problem 1 :

Find the nature of the roots of the following equations

2x² + 3x + 1 = 0

Solution

Problem 2 :

Find the nature of the roots of the following equations

6x² = 7x + 5

Solution

Problem 3 :

Find the nature of the roots of the following equations

3x² + 7x - 2 = 0

Solution

Problem 4 :

Find the nature of the roots of the following equations

√2x² + 3x - √8 = 0

Solution

Problem 5 :

Show that the roots of the following equations are rational

a(b – c)x² + b(c – a)x + c(a – b) = 0

Solution

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