Question

Determine the nature of the roots for the following quadratic equations 

(i) 15.x² + 11.x + 2 = 0 

(ii) x² – x – 1 = 0 

(iii) √2t² – 3t + 3√2 = 0 

(iv) 9y² – 6√2y + 2 = 0 

(v) 9a² b² x² – 24abcdx + 16c² d² = 0, a ≠ 0, b ≠ 0

Comments

Bro i want ans for the questions i asked pls help me bro i am a slow learner

Answer 1

(i) 15x² + 11x + 2 = 0 comparing with ax² + bx + c = 0. 

Here a = 15, 6 = 11, c = 2. 

Δ = b² – 4ac 

= 11² - 4 x 15 x 2 

= 121 – 120 

= 1 > 1. 

∴ The roots are real and unequal.

(ii) x² – x – 1 = 0, 

Here a = 1, b = -1, c = -1.

Δ = b² – 4ac 

= (-1)² – 4 x 1 x -1 

= 1 + 4 = 5 > 0. 

∴ The roots are real and unequal.

(iii) √2t² – 3t + 3√2 = 0 

Here a = √2, b = -3, c = 3√2

Δ = b² – 4ac 

= (-3)² – 4 x √2 x 3√2 

= 9 – 24 = -15 < 0. 

∴ The roots are not real.

(iv) 9y² – 6√2y + 2 = 0 

a = 9, b = 6√2, c = 2 

Δ = b² – 4ac = 

(6√2)² – 4 x 9 x 2 

= 36 x 2 – 72 

= 72 – 72 = 0 

∴ The roots are real and equal.

(v) 9a² b² x² – 24abcdx + 16c² d² = 0

Δ = b² – 4ac 

= (-24abcd)² – 4 x 9a² b² x 16c² d² 

= 576a² b² c² d² – 576a² b² c² d² = 0 

∴ The roots are real and equal.