Question

If the squared difference of the zeroes of quadratic polynomial p(x)=x2 +3x +k is k. Find k.

Answer 1

The roots (zeros) of a quadratic function is given by:
$x = \frac{-b + \sqrt{b^2+4ac} }{2a}$ and $x = \frac{-b - \sqrt{b^2+4ac} }{2a}$

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:
$k=[\frac{-b + \sqrt{b^2+4ac} }{2a}-(\frac{-b + \sqrt{b^2+4ac} }{2a})]^2$
$k = (\frac{2 \sqrt{b^2+4ac} }{2a})^2$
$k = \frac{b^2 - 4ac}{a^2}$
$k=\frac{3^2 - 4(1)(k)}{1^2}$
$9 - 4k - k = 0$
$5k = 9$
$k = \frac{9}{5}$

Answer 2

Answer: k= 9/5

Hope it helps