Question

Find the product of the zeros of a polynomial p(x) = x^2 + 2x − 8​

Answer 1

Answer:

-8

Step-by-step explanation:

p(x)= x^2+2x-8

a=1,b=2,c=-8

product of zeroes = c/a = -8/1= -8

sum of zeroes = -b/a = -2/1 = -2

hope it helps frnd..

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Product\:of\:zeroes=-8}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {x}^{2} + 2x - 8 = 0 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Product \: of \: zeroes = ?$

• According to given question :

$\tt \circ \: Let \: zeroes \: be \: \alpha \: and \: \beta \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Product \: of \: zeroes = \frac{c}{a} \\ \\ \tt: \implies \alpha \beta = \frac{ - 8}{1} \\ \\ \green{\tt: \implies \alpha \beta = - 8} \\ \\ \bold{Alternate \: method : } \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies x = \frac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times ( -8)} }{2 \times 1} \\ \\ \tt: \implies x = \frac{ - 2 \pm \sqrt{4 + 32} }{2} \\ \\ \tt: \implies x = \frac{ - 2 \pm6}{2} \\ \\ \green{\tt: \implies x = - 4 \: and \: 2} \\ \\ \tt \circ \: \alpha = - 4 \\ \\ \tt \circ \: \beta = 2 \\ \\ \bold{For \: Product \: of \: zeroes} \\ \tt: \implies \alpha \beta = - 4 \times 2 \\ \\ \green{\tt: \implies \alpha \beta = - 8}$