Skip to content
dronacharya.ai
← JEE Main 2026 · 5 Apr · Shift 2
MathematicsSingle correct+4 / -1Question 1 of 75

JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 1

Let α,β\alpha,\beta be the roots of the equation x2−x+p=0x^2-x+p=0 and γ,δ\gamma,\delta be the roots the equation x2−4x+q=0x^2-4x+q=0; p,q∈Zp,q\in\mathbb Z. If α,β,γ,δ\alpha,\beta,\gamma,\delta are in G.P., then ∣p+q∣|p+q| equals :

Choose one option
Answer and worked solution

Official answer: C

G.P. Write α, αr, αr2, αr3\alpha,\ \alpha r,\ \alpha r^2,\ \alpha r^3. Then:

  • α+β=α(1+r)=1\alpha+\beta=\alpha(1+r)=1.
  • γ+δ=αr2(1+r)=4\gamma+\delta=\alpha r^2(1+r)=4.

Dividing gives r2=4r^2=4.

Integer condition.

  • r=2r=2: α=13\alpha=\tfrac13 and p=α2r=29p=\alpha^2r=\tfrac29, not an integer.
  • r=−2r=-2: α=−1\alpha=-1, p=α2r=−2p=\alpha^2r=-2 and q=α2r5=−32q=\alpha^2r^5=-32.

So ∣p+q∣=34|p+q|=34.

(C)

Topics:Roots and coefficientsGeometric progression
Next question →