Home
Class 11
MATHS
The equation a x^2+b x+c=0 has real and...

The equation `a x^2+b x+c=0` has real and positive roots. Prove that the roots of the equation `a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0` re real and positive.

Promotional Banner

Similar Questions

Explore conceptually related problems

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If a

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

If a, b are real then show that the roots of the equation (a-b)x^(2)-6(a+b)x-9(a-b)=0 are real and unequal.

If a,b and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1//c dot

If the roots of the equation x^(2)+2bx+c=0 are alpha" and "beta, " then "b^(2)-c =

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

Prove that the equation x^(2)(a^(2)b^(2))+2x(ac+bd)+(c^(2)+d^(2))=0 has no real root if adnebc .