If a+b+c=0 , then the roots of the equation 4ax2+3bx+2c=0 are

Question

If a+b+c=0 , then the roots of the equation 4ax2+3bx+2c=0 are (A) equal (B) imaginary (C) real (D) None of these

Tardigrade Admin · Accepted Answer

Given, a+b+c=0 Let the roots of the equation 4 a x2+3 b x+2 c=0 are α and β Now, D=b2-4 a c =9 b2-4(4 a)(2 c) =9 b2-32 a c =9(a+c)2-32 a c Hence, roots are real.

Q. If $a + b + c = 0$ , then the roots of the equation $4 a x^{2} + 3 b x + 2 c = 0$ are

equal

imaginary

real

None of these

Given, $a + b + c = 0$
Let the roots of the equation $4 a x^{2} + 3 b x + 2 c = 0$ are $α$ and $β$
Now, $D = b^{2} - 4 a c$
$= 9 b^{2} - 4 (4 a) (2 c)$
$= 9 b^{2} - 32 a c$
$= 9 (a + c)^{2} - 32 a c$
Hence, roots are real.

Q. If a+b+c=0 , then the roots of the equation 4ax2+3bx+2c=0 are