Question

X=-
VEXERCISE 4.3
1. Find the roots of the following quadratic equations, if they exist, by the method
completing the square:
(1) 2x² - 7x +3=0
(ii) 2x² + x - 4= 0
(i) 4x² +43x+3 = 0
(iv) 2x2 + x +4= 0​

Answer 1

Step-by-step explanation:

2x2 – 7x +3 =0

Dividing by coefficient of x2, we get

Adding and subtracting the square of

Use the formula (a-b)2 = a2 + b2 - 2ab to get,

So,

When,

When,

Hence the value of x is 3 and

ii) 2x2 + x – 4 = 0

Dividing by coefficient of

Adding and subtracting the square of

Use the formula (a+b)2 = a2 + b2 + 2ab to get,

iii)

Divide the whole equation by 4 to get,

Add and subtract the square of half of the coefficient of x,

Use the formula (a+b)2 = a2 + b2 + 2ab to get,

∴ Roots of equation are = x =

iv) 2x2 + x + 4

Divide by coefficient of

Adding and subtracting the square of coefficient of x we get,

Use the formula (a+b)2 = a2 + b2 +2ab to get,

Square of a number cannot be negative, Hence roots of the given equation do not exist.