Question

If alpha and beta are zeros and the quadratic polynomial f (x) = x²
− x − 4, then the

value of 1/alpha + 1/beta - alpha beta is

a)15/4
b)-15/4
c)4 d)15​

Answer 1

LET 'A' AND 'B' be the roots / zeros of equation ,

=> f (x) = x² - x - 4

=> Then , sum of roots = - ( coefficient of x ) / coefficient of x²

=> A + B = - ( -1 ) / 1 = 1 .......... (1)

=> Product of roots = Constant / coefficient of x²

=> AB = (-4) / 1 = -4 ......... (2)

Now ,

1 / A + 1 / B - AB

=> ( 1/A + 1/B ) - AB

=> { ( B + A ) / AB } - AB

=> 1 / (-4) - (-4)

=> -1/4 + 4 = (-1+16) / 4 = 15/4

Answer is 15/4..