4. The sum of the zeroes of a quadratic polynomial is 15 4 and their product​

Question

4. The sum of the zeroes of a quadratic polynomial is 15

4

and their product​

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Emery 1 month 2021-08-17T15:59:15+00:00 1 Answer 0 views 0

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    2021-08-17T16:00:52+00:00

    Answer:

    ATQ

    \alpha + \beta = \frac{15}{4}

    \alpha \beta = 3

    We know that the polynomial is of the form

    P(x) = x^{2} – (\alpha + \beta)x + \alpha \beta

    P(x) = x^{2} – (\frac{15}{4} )x + 3

    P(x) = x^{2} – \frac{15x}{4} + 3

    P(x) = \frac{4x^{2} – 15x + 12}{4}

    As we know that P(x) is always equal to 0

    Therefore

    0 = \frac{4x^{2} – 15x + 12}{4}

    0 = 4x^{2} – 15x + 12

    Therefore the polynomial is P(x) = 4x^{2} – 15x + 12

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