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(A) For a quadratic polynomial $ax^2 + bx + c$,the sum of zeros $\alpha + \beta = -b/a$ and the product of zeros $\alpha\beta = c/a$.Given the polynom

Vedclass · Accepted Answer

$3/2$

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(A) For a quadratic polynomial $ax^2 + bx + c$,the sum of zeros $\alpha + \beta = -b/a$ and the product of zeros $\alpha\beta = c/a$.Given the polynomial $P(x) = x^2 - 3x + 2k$,we have $a = 1$,$b = -3$,and $c = 2k$.Thus,$\alpha + \beta = -(-3)/1 = 3$ and $\alpha\beta = 2k/1 = 2k$.According to the problem,$\alpha + \beta = \alpha\beta$.Substituting the values,we get $3 = 2k$.Therefore,$k = 3/2$.

If $\alpha$ and $\beta$ are the zeros of the polynomial $P(x) = x^2 - 3x + 2k$ and $\alpha + \beta = \alpha\beta$,then the value of $k$ is:

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