Question

If a,b,cϵ R and 1 is a root of the equation a$x^2$ + bx + c = 0 then the equation 4 a$x^2$+ 3 bx + 2c = 0, c ≠ 0 has roots which are :

• A. Rational
• B. Imaginary
• C. Real and equal
• D. Real and distinct

Answer 1

The correct option is D

Real and distinct

1is root of a$x^2$+bx+c=0 => a+b+c=0

Then 2^nd equation , D= 9$b^2$ – 32ac = 9${(a+c)}^2$ – 32ac

=$c^2${9${\left(\frac{a}{c}\right)}^2$ -14($\frac{a}{c}$)+9}$>$0

=> roots are real and distinct