Question

x®-4x+4=0
3. Determine the nature of roots of the following quadratic equations.
(1) x² - 4x + 4 = 0 (2) 2y2 - 7y + 2 = 0 (3) m2 + 2m + 9 =​

Answer 1

Answer:

Comparing the above equation with ax2 + bx + c = 0, we get a = 1,b = -4, c = 4 ∴ ∆ = b2 – 4ac = (- 4)2 – 4 × 1 × 4 = 16 – 16 ∴ ∆ = 0 ∴ Roots of the given quadratic equation are real and equal. ii. 2y2 – 7y + 2 = 0 Comparing the above equation with ay + by + c = 0, we get a = 2, b = -7, c = 2 ∴ ∆ = b2 – 4ac = (- 7)2 – 4 × 2 × 2 = 49 – 16 ∴ ∆ = 33 ∴ ∆ > 0 ∴ Roots of the given quadratic equation are real and unequal. iii. m2 + 2m + 9 = 0 Comparing the above equation with am2 + bm + c = 0, we get a = 1,b = 2, c = 9 ∴ ∆ = b2 – 4ac = (2)2 – 4 × 1 × 9 = 4 – 36 ∴ ∆ = -32 ∴ ∆ < 0 ∴ Roots of the given quadratic equation are not real.Read more on Sarthaks.com - https://www.sarthaks.com/843800/determine-the-nature-of-roots-of-the-following-quadratic-equations-4x-4-ii-2y-7y-0-iii-m-2-2m-9