Question

K. If the A.M. of the roots of a quadratic equation is and A.M. of their reciprocals is then the quadratic equation is - (A) 5x² - 8x + 7 = 0 (B) 5x² - 16x + 7 = 0) (C) 7x- 16x + 5 =0(D) 7x?+ 16x + 5 = 0

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

Lit ( alpha, B ) the roots [ begin{array}{l} frac{alpha+beta}{2}=frac{8}{5} x+B=16 / 5 end{array} quad frac{frac{1}{alpha}+frac{1}{beta}}{2}=frac{8}{7} ] ( L ) [ frac{1}{x}+frac{1}{p}=frac{16}{7} ] Pun ob roots [ x+beta=frac{16}{7}(alpha beta) ] Noduct of rooks ( quad ) t ( quad alpha beta=frac{7}{16}left(frac{16}{5}right)=frac{7}{5} ) Quadnatic ( 2 q^{n} ) is ( x^{2}-(operatorname{sun}) x+(text { product })=0 ) [ x^{2}-left(frac{16}{3}right) x+left(frac{7}{5}right)=0 ] A ( 5 x^{2}-16 x+7=0 )