If a and Beta are the zero of the the polynomial x² + 6x + 5 then a² + B² + 2aB =

Question

If a and Beta are the zero of the the polynomial x² + 6x + 5 then a² + B² + 2aB =

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Quinn 4 weeks 2021-08-19T06:14:41+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-19T06:15:57+00:00

    Answer:

    f(x)=x2-6x+k;

    by comparing this eq. with ax2+bx+c = 0;

    we get a = 1, b = -6  and c = k;

    Suppose the roots of the equation is alpha and beta:

    alpha + beta = -b/a

    alpha+beta = 6/1;

    alpha*beta = c/a;

    alpha*beta = k

    we know that:

    (a+b)2 = a2+b2+2ab ;

    Not putting the values in above eq.;

    (6)2 = 40 + 2k;

    36 – 40 = 2k;

    -4 = 2k;

    k= -2

    Step-by-step explanation:

    0
    2021-08-19T06:16:30+00:00

    Answer:

    The answer is 36.

    Step-by-step explanation:

    We are given the equation x^2+6x+5 whose roots are \alpha and \beta

    We have to find \alpha^{2}+2\alpha\beta+\beta^{2}

    Recall the algebraic identity \left(a+b\right)^{2}=a^{2}+2ab+b^{2}

    Hence, \alpha^{2}+2\alpha\beta+\beta^{2} can be written as (\alpha+\beta)^2

    Here, \alpha+\beta is the sum of zeroes, and the sum of zeroes of a quadratic equation is \frac{-b}{a}.

    Hence, our required answer must be (\frac{-b}{a})^2

    That is, (-6)^2

    Which happens to be 36.

    Hence, your required answer is 36.

    Hope it helps you.

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