PYQ Vault
EbooksTutor

A linear HCF of two quadratics given: find k or the unknown coefficients

This type of question, asked 5 times: CDS 2 2017, CDS 1 2020, CDS 1 2021, CDS 2 2022, CDS 1 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    20
    If the HCF of polynomials f(x)=(x−1)(x2+3x+a)f(x) = (x - 1) (x^2 + 3x + a) and g(x)=(x+2)(x2+2x+b)g(x) = (x + 2) (x^2 + 2x + b) is (x2+x−2)(x^2 + x - 2), then what are the values of aa and bb respectively ?

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2020

    14
    If (x+k)(x + k) is the HCF of x2+5x+6x^{2} + 5x + 6 and x2+8x+15x^{2} + 8x + 15, then what is the value of kk ?

    Tap an option to check your answer.

  3. Question 3

    CDS 1 2021

    14
    If (x−k)(x - k) is the HCF of x2+ax+bx^2 + ax + b and x2+cx+dx^2 + cx + d, then what is the value of kk?

    Tap an option to check your answer.

  4. Question 4

    CDS 2 2022

    7
    If (x+k)(x + k) is the HCF of x2+px+qx^2 + px + q and x2+qx+px^2 + qx + p, where p≠qp \ne q, then what is the value of k ?

    Tap an option to check your answer.

  5. Question 5

    CDS 1 2026

    6
    If (x−5)(x - 5) is the HCF of x2−x−px^2 - x - p and x2−qx−10x^2 - qx - 10, then what is the value of (p+q)(p + q) ?

    Tap an option to check your answer.