Question

Find the zeros of the polynomial v2+4√3v-15

Answer 1

v*2 +4/3v -15

v*2 +(5/3v-/3v) -15

v*2+5/3v -/3v-15

v(v+5/3) -/3(v+5/3)

(v+5/3) (v-/3)

v+5/3=0

v=-5/3

v-/3=0

v=/3

5/3 and /3 are the zeros of the polynomial

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Assumption

f(v) = v² + 4√3v - 15

★We have

a = 1

b = 4√3

c = -15

f(v) = v² + 5√3v - √3v - 15

f(v) = v(v + 5√3) - √3(v + 5√3)

f(v) = (v - √3)(v + 5√3)

v = √3

v = -5√3

★Zeroes are √3 and -5√3

★Sum of zeroes = α + β

$\tt{\rightarrow\alpha+\beta=-\dfrac{b}{a}}$

$\tt{\rightarrow\sqrt{3}+(-5\sqrt{3}=-\dfrac{4\sqrt{3}}{1}}$

$\tt{\rightarrow -4\sqrt{3}=\dfrac{-4\sqrt{3}}{1}}$

⇒ -4√3 = -4√3

★Product of Zeroes = α × β

$\tt{\rightarrow\alpha\times\beta=-\dfrac{c}{a}}$

$\tt{\rightarrow(\sqrt{3})(-5\sqrt{3})=-\dfrac{15}{1}}$

⇒ -15 = -15

$\Large{\fbox{Hence\;Verified}}$