If the roots of ax2-bx-c-0 are - - and the roots of AX2 -Bx -C - 0 are - - k- - - k- Then B2 - 4AC b2 - 4ac is equal to

The correct option is B (Aa )^2 α ,β are the roots of ax^2+bx+c=0 α β=√(b^2 4ac)a α k,β k are the roots of Ax^2+Bx+C=0 α k ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Purely Real

If the roots ...

Question

If the roots of $a x^{2} + b x + c = 0$ are $α, β$ and the roots of $A X^{2} + B x + C = 0$ are $(α - k), (β - k)$ . Then $(\frac{B^{2} - 4 A C}{b^{2} - 4 a c})$ is equal to

0

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

1

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

(\frac{A}{a})^{2}

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

(\frac{a}{A})^{2}

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

Open in App

Solution

The correct option is B $(\frac{A}{a})^{2}$
$α, β$ are the roots of $a x^{2} + b x + c = 0$
$α - β = \frac{\sqrt{b^{2} - 4 a c}}{a}$
$α - k, β - k$ are the roots of $A x^{2} + B x + C = 0$
$α - k - (β - k) = \frac{\sqrt{B^{2} - 4 A C}}{A}$
$⟹ α - β = \frac{\sqrt{B^{2} - 4 A C}}{A} ⟹ \frac{\sqrt{b^{2} - 4 a c}}{a} = \frac{\sqrt{B^{2} - 4 A C}}{A} ⟹ \frac{B^{2} - 4 A C}{b^{2} - 4 a c} = (\frac{A}{a})^{2}$

Suggest Corrections

Similar questions

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. If

α

β

are roots of

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

and

D = b^{2} - 4 a c

, and

S_{n} = 1 + α^{n} + β^{n}

then

∣ ∣ ∣ ∣ \begin{matrix} S_{0} & S_{1} & S_{2} S_{1} & S_{2} & S_{3} S_{2} & S_{3} & S_{4} \end{matrix} ∣ ∣ ∣ ∣

Q. In the quadratic equation

a x^{2} +

+ c = 0

, if

Δ = b^{2} - 4 a c

and

α + β, α^{2} + {β^{2}, α}^{3} + β^{3}

are in G.P. where

α, β

are the roots of

a x^{2} +

+ c = 0

, then

Q. If

α, β

are the roots of

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

and

α + β, α^{2} + β^{2}, α^{3} + β^{3}

are in G.P., where

△ = b^{2} - 4 a c

, then

Q. Let

α, β

be roots of the equation

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

and

Δ = b^{2} - 4 a c

. If

α + β, α^{2} + β^{2}, α^{3} + β^{3}

are in

G P

, then

Join BYJU'S Learning Program

If the roots of ax2+bx+c=0 are α,β and the roots of AX2+Bx+C=0 are (α−k),(β−k). Then (B2−4ACb2−4ac) is equal to

The correct option is B (Aa)2α,β are the roots of ax2+bx+c=0α−β=√b2−4acaα−k,β−k are the roots of Ax2+Bx+C=0α−k−(β−k)=√B2−4ACA⟹α−β=√B2−4ACA⟹√b2−4aca=√B2−4ACA⟹B2−4ACb2−4ac=(Aa)2

If the roots of $a x^{2} + b x + c = 0$ are $α, β$ and the roots of $A X^{2} + B x + C = 0$ are $(α - k), (β - k)$ . Then $(\frac{B^{2} - 4 A C}{b^{2} - 4 a c})$ is equal to