Home
Class 12
MATHS
If a lt b lt c lt d then show that (x-a)...

If `a lt b lt c lt d` then show that `(x-a)(x-c)+3)x-b)(x-d)=0` has real and distinct roots.

Text Solution

Verified by Experts

The correct Answer is:
T
Promotional Banner

Topper's Solved these Questions

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 2 (Fill In The Blanks)|3 Videos
  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 3|21 Videos
  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 2|66 Videos
  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos
  • TRIGONOMETRICAL EQUATIONS

    ML KHANNA|Exercise SELF ASSESSMENT TEST |27 Videos

Similar Questions

Explore conceptually related problems

If a

If a, b, c, d in R such that a lt b lt c lt d, then roots of the equation (x-a)(x-c)+2(x=b)(x-d) = 0

If (a+b+c)>0 and a < 0 < b < c, then the equation a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-c)=0 has (i) roots are real and distinct (ii) roots are imaginary (iii) product of roots are negative (iv) product of roots are positive

lf 0 < a < b < c < d, then the quadratic equation ax^2 + [1-a(b+c)]x+abc-d=0 A) Real and distinct roots out of which one lies between c and d B) Real and distinct roots out of which one lies between a and b C) Real and distinct roots out of which one lies between b and c (D) non -real roots

If a lt b lt c lt d lt e and f(x) =(x-a)^(2) (x-b) (x -c) (x-d) (x-e ) which of the following is true?

Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt c , then f(x) = (x-a)(x-b)(x-c) -A^(2)(x-a)-B^(2)(x-b)-C^(2)(x-c) has exactly one real root. Statement-2: If f(x) is a real polynomical and x_(1), x_(2) in R such that f(x_(1)) f(x_(2)) lt 0 , then f(x) has at least one real root between x_(1) and x_(2)