Question

give answer with solution... ​

Answer 1

$\large\bf\underline{Question :-}$

• Find the zeroes of √3x² + 10x + 7√3.

$\large\bf\underline{Given:-}$

• p(x) = √3x² + 10x + 7√3

$\large\bf\underline {To \: find:-}$

• zeroes of the given polynomial.

$\huge\bf\underline{Solution:-}$

$\bf \: \dag \: \rm \: p(x) = \sqrt{3} {x}^{2} + 10x + 7 \sqrt{3} \\ \\ \dashrightarrow \rm \: \sqrt{3} {x}^{2} + 3x + 7x + 7 \sqrt{3} \\ \\ \dashrightarrow \rm \: \sqrt{3} x(x + \sqrt{3} ) + 7(x + \sqrt{3} ) \\ \\ \dashrightarrow \rm \: ( \sqrt{3} x + 7)(x + \sqrt{3} ) \\ \\ \dashrightarrow \bf \: x = \frac{ - 7}{ \sqrt{3} } \: or \: \: x = - \sqrt{3}$

$\underline{ \bf \dag \: \: Verification : - }$

★ p(x) = √3x² + 10x + 7√3

• a = √3
• b = 10
• c = 7√3

Let α and β are the zeroes of the given polynomial.

let α = -7/√3 and β = -√3

• sum of zeroes = -b/a

$\rightarrowtail \: \rm \frac{ - 7}{ \sqrt{3} } +( - \sqrt{3} ) = \frac{ - 10}{ \sqrt{3} } \\ \\ \rightarrowtail \: \rm \frac{ - 7 - 3}{ \sqrt{3} } = \frac{ - 10}{ \sqrt{3} } \\ \\ \rightarrowtail \: \rm \frac{ - 10}{ \sqrt{3} } = \frac{ - 10}{ \sqrt{3} }$

• Product of zeroes = c/a

$\rightarrowtail \: \rm \frac{ - 7}{ \sqrt{3} } \times ( - \sqrt{3} ) = \frac{ 7 \sqrt{3} }{ \sqrt{3} } \\ \\ \rightarrowtail \: \rm \frac{7 \sqrt{3} }{ \sqrt{3} } = \frac{7 \sqrt{3} }{ \sqrt{3} } \\ \\ \rightarrowtail \: \rm7 = 7$

LHS = RHS

hence Verified

Answer 2

your answer refer to the attachment.