Question

If p and q are zeroes of the polynomial x²+6x+2 then the value of 1/p +1/q is​

Answer 1

Answer:

{\underline{\underline{\maltese\textbf{\textsf{\red{Question}}}}}}✠Question

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

\begin{gathered}\end{gathered}

{\underline{\underline{\maltese\textbf{\textsf{\red{Solution}}}}}}✠Solution

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

{: \implies{\sf\bigg({\dfrac{x - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 2x}{3}} \bigg)}}:⟹(2x−(6×2))=(3(8×3)−2x)

{: \implies{\sf\bigg({\dfrac{x - 12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 2x}{3}} \bigg)}}:⟹(2x−12)=(324−2x)

By cross multiplication

: \implies\sf{3(x - 12) = \bf{2(24 - 2x)}}:⟹3(x−12)=2(24−2x)

: \implies\sf{3x - 36 = \bf{48 - 4x}}:⟹3x−36=48−4x

: \implies\sf{4x - 3x = \bf{48 -36}}:⟹4x−3x=48−36

: \implies\sf{x = \bf{12}}:⟹x=12

{\dag{\underline{\boxed{\sf{x =12}}}}}†x=12

Hence, The value of x is 12.

\begin{gathered}\end{gathered}

{{\underline{\underline{\maltese\textbf{\textsf{\red{Verification}}}}}}}✠Verification

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

Substituting the value of x

: \implies{\sf\bigg({\dfrac{12}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2 \times 12}{3}} \bigg)}:⟹(212−6)=(8−32×12)

: \implies{\sf\bigg({\dfrac{12}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{24}{3}} \bigg)}:⟹(212−6)=(8−324)

{: \implies{\sf\bigg({\dfrac{12 - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 24}{3}} \bigg)}}:⟹(212−(6×2))=(3(8×3)−24)

{: \implies{\sf\bigg({\dfrac{12 -12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 24}{3}} \bigg)}}:⟹(212−12)=(324−24)

{: \implies{\sf\bigg({\dfrac{0}{2}}\bigg) = \bf\bigg({\dfrac{0}{3}} \bigg)}}:⟹(20)=(30)

: \implies\sf{0} = \bf{0}:⟹0=0

\dag{\underline{\boxed{\sf{LHS=RHS}}}}†LHS=RHS

Hence Verified!!

Answer 2

Step-by-step explanation:

${x }^{2} + 6x + 2 \\ a = 1, \: b = 6, \: c = 2 \\ \alpha = p, \: \beta = q \\ D = {b}^{2} - 4ac \\ = {6}^{2} - 4 \times 1 \times 2 \\ = 36 - 8 \\ = 28 \\ \alpha = \frac{-b + \sqrt{D} }{2a}, \: \: \beta = \frac{- b- \sqrt{D} }{2a} \\ p= \frac{-6 + \sqrt{28} }{2}, \: \: q= \frac{- 6- \sqrt{28} }{2} \\ p= \frac{-6 + \sqrt{2 \times 2 \times 7} }{2}, \: \: q= \frac{- 6- \sqrt{2 \times 2 \times 7} }{2} \\ p= \frac{-6 + 2\sqrt{7} }{2}, \: \: q= \frac{- 6- 2\sqrt{7} }{2} \\ p= \frac{2(-3 + \sqrt{7} )}{2}, \: \: q= \frac{2(- 3- \sqrt{7} )}{2} \\ p= -3+ \sqrt{7} , \: \: q= - 3- \sqrt{7} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \blue{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$