Question Number 1041 by tera last updated on 22/May/15

if the roots of the equation ax^2 +5x−2=0 is 2 and b.    then 4a^2 −4ab+b^2 =...

Answered by prakash jain last updated on 23/May/15

Since x=2 is a root (x−2) is a factor of  ax^2 +5x−2  Put x=2  4a+10−2=0⇒a=−2  −2x^2 +5x−2=0  −2x^2 +4x+x−2=0  −(2x−1)(x−2)=0  Roots at 2 and (1/2), hence b=(1/2)  4a^2 −4ab+b^2 =4(−2)^2 −4(−2)((1/2))+((1/2))^2   =16+4+(1/4)=((81)/4)

Commented bytera last updated on 23/May/15

thank you sir

Answered by prakash jain last updated on 22/May/15

sum of roots 2+b=((−5)/a)⇒2a+ab=−5  product of roots 2b=((−2)/a)⇒ab=−1  2a+ab=−5⇒2a−1=−5⇒a=−2  ab=−1⇒b=(1/2)  put values in 4a^2 −4ab+b^2