Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2004 · Mathematics · Quadratic Equation

If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0 , then its...

If (1−p)(1-p) is a root of quadratic equation x2+px+(1−p)=0x^2+p x+(1-p)=0, then its roots are

Options

  1. A0,1
  2. B−1,2-1,2
  3. C0,−10,-1
  4. D−1,1-1,1

Correct answer

C. 0,−10,-1

Step-by-step solution

(3)(1−p)2+p(1−p)+(1−p)=0( since (1−p) is a root of the equation x2+px+(1−p)=0)⇒(1−p)(1−p+p+1)=0⇒2(1−p)=0⇒(1−p)=0⇒p=1 sum of root is α+β=−p and product αβ=1−p=0 (where β=1−p=0)⇒α+0=−1⇒α=−1⇒ Roots are 0,−1\begin{aligned}& (1-p)^2+p(1-p)+(1-p)=0 \quad\left(\text{ since }(1-p) \text{ is a root of the equation }x^2+p x+(1-p)=0\right) \\ & \Rightarrow(1-p)(1-p+p+1)=0 \\ & \Rightarrow 2(1-p)=0 \Rightarrow(1-p)=0 \Rightarrow p=1 \\ &\text{ sum of root is } \alpha+\beta=-p \text{ and product } \alpha \beta=1-p=0 \quad \text{ (where } \beta=1-p=0) \\ & \Rightarrow \alpha+0=-1 \Rightarrow \alpha=-1 \Rightarrow \text{ Roots are }0,-1 \end{aligned}
Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 +… JEE Advanced 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n ∈ ℝ .… JEE Main 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be… JEE Main 2026Let e_1 and e_2 be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets \ a… JEE Main 2026Let α, β be the roots of the equation x^2 - x + p = 0 and γ, δ be the roots the equation… JEE Main 2026Let a, b ∈ ℂ . Let α, β be the roots of the equation x^2 + ax + b = 0 . If β - α = 11 and… JEE Main 2026Let A, B , where A, B ∈ (-(π)/(2), (π)/(2)) , be the roots of the quadratic equation x^2… JEE Main 2026If α=1 and β=1+i 2 , where i= -1 are two roots of the equation x^3+ax^2+bx+c=0 , a,b,c ∈… JEE Main 2026If the quadratic equation (λ+2)x^2-3λ x+4λ=0 , λ ≠ -2 , has two positive roots, then the… JEE Main 2026Let α, β be the roots of the equation x^2 - 3x + r = 0 , and (α)/(2), 2β be the roots of… JEE Main 2026Let a, b, c ∈ \ 1, 2, 3, 4\ . If the probability, that ax^2 + 2 2 \,bx + c > 0 for all x… JEE Main 2026Let S=\ x^ 3 +a x^ 2 +b x+c: a, b, c ∈ ~N. and .a, b, c ≤ 20\ be a set of polynomials.… JEE Main 2026If α, β , where α<β , are the roots of the equation λ x^ 2 -(λ+3) x+3=0 such that… JEE Main 2026The smallest positive integral value of a , for which all the roots of x^ 4 -a x^ 2 +9=0… JEE Main 2026The sum of all the real solutions of the equation _ (x+3) (6 x^ 2 +28 x+30)=5-2 _ (6… JEE Main 2026 Full Quadratic Equation list Quadratic Equation JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs