Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficient. 5x Square + 10x ​

Answer 1

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$Let \: \: p(x) \: \: = \: \: 5 {x}^{2} + 10x$

$For \: finding \: roots \: of \: the \: solution, \\ let \: \: p(x) = 0$

$5 {x}^{2} + 10x = 0$

$5x(x + 2) = 0$

$5x = 0 \: \: \: \: and \: \: \: \: x + 2 = 0$

$x = 0 \: \: \: \: and \: \: \: \: x = - 2$

$Sum \: \: of \: \: zeroes = \alpha + \beta = - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

$- 2 + 0 = - \frac{10}{5}$

$- 2 = - 2$

$l.h.s \: = \: r.h.s \: \: \: \: verified$

$Product \: \: of \: \: zeroes = \alpha \times \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$- 2 \times 0 = \frac{0}{5}$

$0 = 0$

$l.h.s \: = \: r.h.s \: \: \: \: verified$

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