Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

If P(x)=a x^2+b x+c leaves a remainder of 4 when divided by x , a remainder of 3 when divided by (x+1) and a remainder of 1 when divided by (x-1) then P(2) is

Options

Correct answer

D. -6

Step-by-step solution

aligned & P(x)=a x^2+b x+c & P(x)=Q₁(x)+4=Q₂(x+1)+3=Q₃(x-1)+1 & P(0)=c=4 aligned aligned & P(-1)=a-b+4=3(b-a=1) & P(1)=a+b+4=1(b+a=3) & b=-1, a=-2 aligned aligned & P(x)=2 x^2-x+4 & P(2)=-8-2+4=-6 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. List-I List-II (P) If and are the distinct roots of the equation x^2 + x + 1 = 0 , then th 2026 Let 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 2026 Consider 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 2026 Let 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: 2026 Let 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 2026 Let , 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 : 2026 Let 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: 2026 Let 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