Question

If the quadratic equation (1 + a2)b2x2 + 2abcx + (c2 - m2) = 0 has equal roots, prove that
c2 = m²(1 + a2).​

Answer 1

Step-by-step explanation:

d=0 for equal roots

b2-4ac =0

solve it bro you will get it

easy question.

good luck

here is the solution for you any doubts you can ask.

Answer 2

Given: A quadratic equation $(1 + a^2)b^2\text { x}^2 + 2abc \text { x }+ (c^2 - m^2) = 0$

To prove: $c^2=m^2(1+a^2)$

Step-by-step explanation:

As we know

$Ax^2+Bx+C=0$ is the general quadratic equation

As $D=B^2-4AC$ where D is  discriminant

D=0 when the quadratic equation has equal roots

So we get

$A= (1+a^2)b^2\\\\B=2abc\\\\C=c^2-m^2$

So

$D= (2abc)^2-4(1+a^2)b^2(c^2-m^2)$

Roots are equal therefore D= 0

$4a^2b^2c^2-4(1+a^2)b^2(c^2-m^2)=0\\\\\Rightarrow 4b^2(a^2c^2-(1+a^2)(c^2-m^2))=0\\\\\Rightarrow (a^2c^2-c^2-a^2c^2+m^2=m^2a^2))=0\\\\\Rightarrow -c^2+m^2+m^2a^2=0\\\\\Rightarrow c^2=m^2a^2+m^2\\\\\Rightarrow c^2=m^2(1+a^2)$

Hence proved the required result that if  $(1 + a^2)b^2\text { x}^2 + 2abc \text { x }+ (c^2 - m^2) = 0$  has equal roots then  $c^2=m^2(1+a^2)$