Question

If alpha and beta are the zeros of polynomial 6x2-7x-3,then form a quadratic polynomial whose zeros are 2alpha and 2 beta​

Answer 1

Solution:—

We have ,

Sum of roots = - ( coefficient of x ) / ( coefficient of x² )

α + ß = - ( - 7 ) / 6

α + ß = 7 / 6.

Now ,

Product of roots = constant term / coefficient of x²

αß = ( - 3 ) / 6

αß = - 1 / 2.

Now a quadratic equation whose zeroes are 2α and 2ß.

= x² - ( sum of roots ) x + ( product of roots )

= x² - ( 2α + 2ß ) x + ( 2α * 2ß )

= x² - ( α + ß ) 2 x + 4 αß

By substituting the values of ( α + ß ) and αß in above step ,

= x² - ( 7 / 6 ) 2 x + 4 ( - 1/ 2 )

= x² - ( 7x / 3 ) - 2

3 x² - 7 x - 6

= ---------------------- = 0

3

= 3 x² - 7 x - 6 .Ans.