Question

) If a and b are the zeros of the quadratic polynomial
f(x)= x2-5x+4, find the value of (1/a + 1/b) –2a b

Answer 1

If a and b are the zeros that means (x+a) and (x+b) are the solutions for the given equation, Remember the product of (x+a) and (x+b) has the form x^2+(a+b)x+ab; which means the given equation x^2-5x+4 has solutions a and b when a+b= -5 and a X b=4; now consider the second part ,(1/a+1/b) can be written as( a+b)/ ab by taking the LCM so the second part now becomes{(a+b)/ab } - 2 ab
we have ab=4 and a+b =-5 Now simply substitute {-5/4}-2X4
=(-5/4)-8=-(37/4) will be the answer.
another way is also there, we can easily  calculate  a and b as -4 and -1.  Now substitute this to the equation (1/a + 1/b) –2a b  you will get same answer!

Answer 2

(1/a+1/b) can be written as( a+b)/ ab by taking the LCM so the second part now becomes{(a+b)/ab } - 2 ab
we have ab=4 and a+b =-5 Now simply substitute {-5/4}-2X4
=(-5/4)-8=-(37/4) will be the answer.
another way is also there, we can easily  calculate  a and b as -4 and -1.  Now substitute this to the equation (1/a + 1/b) –2a b