Question

if the squared difference of the zeros of the quadratic polynomial p(x)=x^2+3x+k is 3. find k

Answer 1

Answer:

k = 45

Step-by-step explanation:

The roots (zeros) of a quadratic function is given by:

x ={-b +{b^2+4ac}}{2a} and x ={-b -{b^2+4ac} }{2a}

The squared difference of the zeros = k, therefor:

If p(x)=x^2+3x+k, written in its standard form of ax^{2} + bx + c, then:

k=[{-b +{b^2+4ac} }{2a}-({-b + {b^2+4ac} }{2a})]^2

k = ({2 {b^2+4ac} }{2a})^2

k = {b^2 - 4ac}{a^2}  

k={3^2 - 4(1)(k)}{1^2}

9 - 4k - k = 0

5k = 9

k ={9}{5}

k=45

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