Question

If alpha and beta are zeroes of polynomial 6 x square - 7x-3 then for a quadratic polynomial where zeroes are 2aplha and 2 beta

Answer 1

Hii mate......

given that:-

6xsquare-7x-3

solution:

6xsquare+2x-9x-3. [middle term split]

=2x(3x+1)-3(3x+1)

=(2x-3)(3x+1)

therefore ,zeroes are :-

alpha = 3/2 and beta = -1/3

according to question given that:-

zeroes:

alpha = 2alpha

= 2(3/2)

= 3

beta = 2(-1/3)

= -2/3

therefore ,required polynomial :-

By using general formula:-

k[x square - (alpha + beta )x + (alpha × beta)] = 0 {k is non - zero constant}

= k[x square - {3+(-2/3)}x + {3 × (-2/3)}]=0

= k[x square - {3-2/3}x + (-2)] =0

= k[x square -(1/3)x -2] = 0

= k[x square -1/3x -2] = 0

therefore , the polynomial is x square -1/3x -2.

Hope its help you.......

= k[x square - {9-2/3}x -2]