If $a, b$ are roots of $A x^{2} + B x + C = 0$ and $a^{2}, b^{2}$ are roots of $x^{2} + p x + q = 0$ then $p$ is equal to:

\frac{B^{2} - 4 A C}{A^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{B^{2} - 2 A C}{A^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{4 A C - B^{2}}{A^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 A C - B^{2}}{A^{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{2 A C - B^{2}}{A^{2}}$
Given that , $a$ and $b$ are roots of $A x^{2} + B x + C = 0$
So, $a + b = - B / A$ .....(i)
$a b = C / A$ .....(ii)
Also, given that $a^{2}$ and $b^{2}$ are roots of $x^{2} + p x + q = 0$
So, $a^{2} + b^{2} = - p$ .....(iii)
$a^{2} b^{2} = q$ .....(iv)
By using identity, $(A + B)^{2} = A^{2} + 2 A B + B^{2}$
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$
Putting values from equation (i), (ii) and (iii), we get
$(- B / A)^{2} = - p + 2 C / A$
$B^{2} / A^{2} = - p + 2 C / A$
$p = 2 C / A - B^{2} / A^{2}$
$p = (2 A C - B^{2}) / A^{2}$

Suggest Corrections

Similar questions

Q. If sin θ and cos θ are the roots of the equation ax² – bx + c = 0, then a, b and c satisfy the relation
(a) a² + b² + 2ac = 0
(b) a² – b² + 2ac = 0
(c) a² + c² + 2ab = 0
(d) a² – b² – 2ac = 0

Q. If sin α and cos α are the roots of the equation

a x^{2} + b x + c = 0,

then

If $α, β$ are the roots of $a x^{2} + b x + c = 0 a n d α + k, β + k$ are the roots of $p x^{2} + q x + r = 0$ , then $\frac{b^{2} - 4 a c}{a^{2} - 4 p r}$ is equal to

Q. What are the roots of the quadratic equation

a x^{2} + b x + c = 0 ?

If b² – 4ac = 0 then The roots of the Quadratic equation ax² + bx + c = 0 are given by :

Join BYJU'S Learning Program

If a,b are roots of Ax2+Bx+C=0 and a2,b2 are roots of x2+px+q=0 then p is equal to:

If $a, b$ are roots of $A x^{2} + B x + C = 0$ and $a^{2}, b^{2}$ are roots of $x^{2} + p x + q = 0$ then $p$ is equal to: