Question

Q.6 Find the roots of the quadratic equations by applying the quadratic formula.
(i) 2x2 - 7x + 3 = 0
(ii) 2x2 - x + 4 = 0
​

Answer 1

Step-by-step explanation:

(I)

Quadratic Equations

Ax2 + Bx + C = 0

A = 2, B = -7 , C = 3

X1 = { - B - root (BxB - 4xAxC)} / 2xA

X2 = { - B + root (BxB - 4xAxC)} / 2xA

X1 = { +7 - root (7x7 - 4x2x3)} / 2x2

X1 = { +7 - root (25)} / 4

X1=(7-5)/4

X1 = 1 / 2

X2 = 3

Answer 2

(i) 2x2 – 7x + 3 = 0  

On comparing the given equation with ax2 + bx + c = 0, we get,

a = 2, b = -7 and c = 3

By using quadratic formula, we get,

x= -b ±√b²- 4ac÷2a

⇒ x = (7±√(49 – 24))/4

⇒ x = (7±√25)/4  

⇒ x = (7±5)/4

⇒ x = (7+5)/4 or x = (7-5)/4

⇒ x = 12/4 or 2/4

∴  x = 3 or 1/2

(ii) 2x2 + x – 4 = 0

On comparing the given equation with ax2 + bx + c = 0, we get,

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

By using quadratic formula, we get,

x= -b ±√b²- 4ac÷2a

⇒x = -1±√1+32/4

⇒x = -1±√33/4

∴ x = -1+√33/4 or x = -1-√33/4