Question

If roots of equation $2x^2+bx+c=0;b,c\in R$, are real distinct then the roots of equation $2c{x}^2+\left(b-4c\right)x+2c-b+1=0$ are

• A. imagnary
• B. equal
• C. real and distinct
• D. can't say

Answer 1

The correct option is C real and distinct

For a given Quadratic Equation,

$a{x}^2+bx+c=0$

$D=b^2-4ac$

Given Equation,

$2x^2+bx+c=0$

$D=b^2-4ac$

$=b^2-4\times 2\times c$

$=b^2-8c$

Now for equation,

$2c{x}^2+(b-4c)x+2c-b+1=0$

$D=b^2-4ac$

$=(b-4c{)}^2-4\times 2c\times (2c-b+1)$

$=b^2+16c^2-8bc-16c^2+8bc-8c$

$=b^2-8c$

We can see that both equation have same discriminant.

Therefore,

both equation have real and distinct roots.