find the zeros of the quadratic polynomial 6x2+29 x+35 and verify the relationship between the zeroes and the coefficient of the polynomial
Answers
To find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coefficient of the polynomial.
Answer:
\large {\red {\underline {\overline {\mid {\sf {Aim:-{\mid }}}}}}}
∣Aim:−∣
To find the zeroes of the quadratic polynomial 6x² - 29x +356x²−29x+35 and verify the relationship between the zeroes and the coefficient of the polynomial.
\large {\red {\underline {\overline {\mid {\sf {Prerequisite \: Concept:-{\mid }}}}}}}
∣PrerequisiteConcept:−∣
\small{\orange {\boxed {\bf {Factorization \: method}}}}
Factorizationmethod
\small{\orange {\boxed {\bf {Sum\: of\: zeroes = \frac{-b}{a}}}}}
Sumofzeroes=
a
−b
\small{\orange {\boxed {\bf {Product \: of \: zeroes = \frac{c}{a}}}}}
Productofzeroes=
a
c
\large {\red {\underline {\overline {\mid {\sf {Calculation:-{\mid }}}}}}}
∣Calculation:−∣
\begin{gathered} Factorizing \: the\: equation, \\ ⇒6x² - 29x + 35 = 0\\ ⇒6x² - 14x - 15x + 35 = 0 \\⇒2x(3x - 7) -5(3x - 7) =0\\ ⇒(2x - 5)(3x - 7) = 0 \\ ⇒x = \frac{5}{2}, \frac{7}{3} \end{gathered}
Factorizingtheequation,
⇒6x²−29x+35=0
⇒6x²−14x−15x+35=0
⇒2x(3x−7)−5(3x−7)=0
⇒(2x−5)(3x−7)=0
⇒x=
2
5
,
3
7
\begin{gathered} Sum\: of \:zeroes = \frac{5}{2} + \frac{7}{3} = \frac{29}{6} \\ Sum \: of \: zeroes,\: by \: coefficients = \frac{-b}{a} = \frac{29}{6} \\ \\ Product \: of \: zeroes = \frac{5}{2} × \frac{7}{3}= \frac{35}{6} \\ Product\: of \: zeroes,\: by \: coefficients = \frac{c}{a} = \frac{35}{6}\\ Hence, \: verified \end{gathered}
Sumofzeroes=
2
5
+
3
7
=
6
29
Sumofzeroes,bycoefficients=
a
−b
=
6
29
Productofzeroes=
2
5
×
3
7
=
6
35
Productofzeroes,bycoefficients=
a
c
=
6
35
Hence,verified