The equation px²+px+3q=1+2x has roots 1/p and q (a) Find the values of p and of q​

Question

The equation px²+px+3q=1+2x has roots 1/p and q

(a) Find the values of p and of q​

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Khánh Gia 6 months 2021-07-23T14:17:04+00:00 1 Answers 25 views 0

Answers ( )

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    2021-07-23T14:18:58+00:00

    Answer:

    p = 2/3

    q = 1/2

    Step-by-step explanation:

    The given equation is ,

    \sf\to px^2 + px + 3q = 1 + 2x

    We can write it as ,

    \sf\to px^2 + px + 3q - 1 -2x=0

    Rearrange the terms ,

    \sf\to px^2 - 2x + px + (3q -1)=0

    This can be written as ,

    \sf\to px^2 + x ( p - 2)  + (3q -1) =0

    Now wrt Standard form of a quadratic equation ,

    \bf \implies ax^2+bx + c = 0

    we have ,

    • a = p
    • b = p – 2
    • c = 3q – 1

    We know that product of zeroes :

    \to \sf q \times \dfrac{1}{p} = \dfrac{3q-1}{p } \\\\\sf\to 3q - 1 = q  \\\\\sf\to 2q = 1  \\\\\sf\to \boxed{ q =\dfrac{1}{2}}

    Sum of roots :

    \to \sf q + \dfrac{1}{p} = \dfrac{2-p}{p}  \\\\\sf\to \dfrac{ qp + 1}{p}= \dfrac{2-p}{p} \\\\\sf\to qp + 1 = 2 - p \\\\\sf\to p/2 + p = 1  \\\\\sf\to 3p/2 = 1  \\\\\sf\to  \boxed{ p =\dfrac{2}{3}}

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