Ifα and β are zeroes ofpolynomíal 6x2-7x-3, then form a quadratic p

1.	Ifα and β are zeroes ofpolynomíal 6x2-7x-3, then form a quadratic polynom twhere zeroes are 2α and 2β
Answer» When a and b are zeroes of 6x² - 7x - 3 a + b = 7/6 ab = -3/6 = -1/2 So, Any equation having 2a and 2b as roots can be written as (x - 2a) ( x - 2b) = 0 = x² - 2( a + b)x + 4ab = 0 = x² - 2 × 7/6 x + 4 × (-1/2) = 0 = x² -7/3 x - 2 = 0 multiply by 3 3x² - 7x - 6 = 0

Ifα and β are zeroes ofpolynomíal 6x2-7x-3, then form a quadratic polynom twhere zeroes are 2α and 2β

Answer»

When a and b are zeroes of 6x² - 7x - 3

a + b = 7/6

ab = -3/6 = -1/2

So, Any equation having 2a and 2b as roots can be written as

(x - 2a) ( x - 2b) = 0

= x² - 2( a + b)x + 4ab = 0

= x² - 2 × 7/6 x + 4 × (-1/2) = 0

= x² -7/3 x - 2 = 0

multiply by 3

3x² - 7x - 6 = 0