Question

8. If a and ß are the zeroes of polynomial 6x2 - 7x-3, then form a polynomial whose
zeroes are 2 a and 2 ß.​

Answer 1

Given :-

α and β are zeroes of 6x² - 7x - 3

To Find :-

Quadratic polynomial whose zero are 2α and 2β

Solution :-

On comparing the given equation with ax² + bx + c. We get,

a = 6

b = -7

c = -3

Sum of zeroes = -b/a

Sum = -(-7)/6

Sum = 7/6

Product of zeroes = c/a

Product = -3/6

Product = -1/2

Now

New Sum of zeroes = 2α + 2β

= 2(α + β)

= 2(7/6)

= 7/3

New Product of zeroes = 2α × 2β

= 4αβ

= 4(-1/2)

= -2

Standard form of a quadratic polynomial = x² - (α + β)x + αβ

x² - (7/3)x + (-2)

x² - 7x/3 - 2

3x² - 7x - 2