If the zero of the polynomial x square – Px plus q are three and two then find the value of p and q

Question

If the zero of the polynomial x square – Px plus q are three and two then find the value of p and q

in progress 0
Ivy 6 days 2021-11-23T00:36:48+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-23T00:37:58+00:00

    Question

    If the zeroes of the polynomial {x}^2 - px + q = 0 are three and two respectively.

    Then find the value of p and q .

    Solution

    In the above question, the following information is given –  

    The zeroes of the polynomial {x}^2 - px + q = 0 are three and two respectively.

    \sf { Let \: the \ required \ Zeroes \ be \ \alpha  \ and \ \beta \  respectively. } \\ \\  \tt{ According \ to \ the \ above \ question - } \\\\\alpha  + \beta   = 3  + 2 = 5\\\\  \sf{ The \ required \ Sum \ Of \Zeroes = \dfrac{ p}{1} = p } \\\\Hence \\\\p = 3 \\\\\sf{ Product \ Of \ Zeroes = \alpha  \times \beta  = 2 \times 3 = 6 } \\\\\sf{ But ,  Product \ Of \ Zeroes = \dfrac{c}{a} = q . } \\\\Hence \\\\q = 6

    0
    2021-11-23T00:38:38+00:00

    Given: The zeros of the polynomial x² – px + q are 3 and 2.

    To find: The value of p and q.

    Answer:

    We know that the general form of a quadratic question is:

    \tt x^2\ -\ (sum\ of\ the\ zeros)x\ +\ (product\ of\ the\ zeros)

    Comparing the given equation with the general form, we get that the sum of the zeros is p and the product is q.

    Let’s take a sample equation.

    ax² + bx + c

    From this, the sum of the zeros is -b/a and the product is c/a.

    Since 3 and 2 are the zeros,

    Sum of the zeros ⇒ 3 + 2 = 5 = p

    Product of the zeros ⇒ 3*2 = 6

    Therefore, p = 5 and q = 6.

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )