Discuss the nature of roots of (i) -x2 + 3x + 1 = 0 (ii) 4x2 – x �

1.	Discuss the nature of roots of (i) -x2 + 3x + 1 = 0 (ii) 4x2 – x – 2 = 0 (iii) 9x2 + 5x = 0
Answer» (i) -x² + 3x + 1 = 0 ⇒ comparing with ax² + bx + c = 0 ∆ = b² – 4ac = (3)² – 4(1)(-1) = 9 + 4 = 13 > 0 ⇒ The roots are real and distinct (ii) 4x² – x – 2 = 0 a = 4, b = -1, c = -2 ∆ = b² – 4ac = (-1)² – 4(4)(-2) = 1 + 32 = 33 > 0 ⇒ The roots are real and distinct (iii) 9x² + 5x = 0 a = 9, b = 5, c = 0 ∆ = b² – 4ac = 5² – 4(9)(0) = 25 > 0 ⇒ The roots are real and distinct

Discuss the nature of roots of (i) -x2 + 3x + 1 = 0 (ii) 4x2 – x – 2 = 0 (iii) 9x2 + 5x = 0

Answer»

(i) -x² + 3x + 1 = 0

⇒ comparing with ax² + bx + c = 0

∆ = b² – 4ac = (3)² – 4(1)(-1) = 9 + 4 = 13 > 0

⇒ The roots are real and distinct

(ii) 4x² – x – 2 = 0

a = 4, b = -1, c = -2

∆ = b² – 4ac = (-1)² – 4(4)(-2) = 1 + 32 = 33 > 0

⇒ The roots are real and distinct

(iii) 9x² + 5x = 0

a = 9, b = 5, c = 0

∆ = b² – 4ac = 5² – 4(9)(0) = 25 > 0

⇒ The roots are real and distinct