Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Consider, f(x)= ( x-10) (x^2-4 x+3 ) (x^2+x+1 ) x^2-16 . Identify which of the following statement(s) is (are) correct.

Options

  1. ANumber of integral values of x for which f(x) 0 is 6 .
  2. BSum of all the integral values of x for which f(x) 0 is -2 .
  3. CNumber of integral values of x for which f(x) 0 is 10 .
  4. DSum of all the integral values of x for which f(x) 0 is 6 .

Correct answer

D. Sum of all the integral values of x for which f(x) 0 is 6 .

Step-by-step solution

f(x)= ( x-10) (x^2-4 x+3 ) (x^2+x+1 ) x^2-16 for f(x) 0 ( x-10) (x^2-4 x+3 ) (x^2+x+1 ) x^2-16 0 aligned & (x-1)(x-3) (x-4)(x+4) 0 & x (-4,1] [3,4) aligned Integral values of x are -3,-2,-1,0,1,3 , i.e., 6 and their sum =-2 . for f(x) 0 ( x-10) (x^2-4 x+3 ) (x^2+x+1 ) x^2-16 0 aligned & (x-1)(x-3) (x-4)(x+4) 0 & x (- ,-4) [1,3] [4, ] aligned Integral values of x are infinite and their sum =1+2+3=6

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. List-I List-II (P) If and are the distinct roots of the equation x^2 + x + 1 = 0 , then th 2026Let a, b, c be positive integers in arithmetic progression such that the equation ax^2 + bx + c = 0 has only integer solutions. Then which of the following statements is (are) TRUE 2026Consider the quadratic equation (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0 , n R . Let be the minimum value of the product of its roots and be the maximum value of the sum of it 2026Let one root of the quadratic equation in x : (k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0 be twice the other. Then the length of the latus rectum of the parabola y^2 = 6kx is equal to: 2026Let e₁ and e₂ be two distinct roots of the equation x^2 - ax + 2 = 0 . Let the sets a R : e₁ and e₂ are the eccentricities of hyperbolas = ( , ) , and a R : e₁ and e₂ are the eccen 2026Let , be the roots of the equation x^2 - x + p = 0 and , be the roots the equation x^2 - 4x + q = 0 ; p, q Z . If , , , are in G.P., then |p + q| equals : 2026Let a, b C . Let , be the roots of the equation x^2 + ax + b = 0 . If - = 11 and ^2 - ^2 = 3i 11 , then ( ^3 - ^3)^2 is equal to: 2026Let A, B , where A, B (- 2 , 2 ) , be the roots of the quadratic equation x^2 - 2x - 5 = 0 . Then 20 ^2 ( A+B 2 ) is equal to: 2026 Full Quadratic Equation list All Most Important Selected Qs for JEE Advanced PYQs