Question

if a & b are zeroes of equation x^2-1=0 , find equation for the zeroes 2a/b & 2b/a​

Answer 1

Solution

Given :-

• x² - 1 = 0

Find :-

• a & b are zeros .

Explanation

Using Formula

★ Sum of zeroes = -(Coefficient of x)/(coefficient of x²)

★Product of zeroes = (constant part)/(coefficient of x²)

Case 1

==> Sum of zeroes = 0/1

==> a + b = 0____________(1)

Case 2.

==> Product of zeroes = 1/1

==> a.b = -1_____________(2)

by equ(1)

==> a = -b_________(3)

keep in equ(2)

==> (-b).(b) = -1

==>b.b = 1

==> b² = 1

==> b = ±1

Keel value of b un equ(3)

When,

• b = 1

Then

• a = -1

When,

• b = -1

Thren,

• a = 1

Since,

• Zeroes of given Equation will be 1,-1 or -1,1

______________________________

Now, Calculate Equation whose zeroes be 2a/b & 2b/a

We take any zeroes, & calculate Equation,

We Take,

• a = 1
• b = -1

Then, Let new zeroes be

• 2a/b = 2×1/(-1) = -2 = p
• 2b/a = 2 ×(-1)/1 = -2 = q

Formula Of Equation

★ x² - (p + q )x + p.q = 0

keep above Values,

==> x² - [ (-2 - 2)x + (-2)(-2) = 0

==> x² + 4x + 4 = 0

Hence

• New Equation will be x² + 4x + 4 = 0

____________________