the šeros of
verify that 2and -3
are the zeroes of
polynomial x2+x-6​

2 thoughts on “the šeros of<br />verify that 2and -3<br />are the zeroes of <br />polynomial x2+x-6​”

1. [tex]{\boxed{\underline{\tt{ \orange{Required \: \: answer \: \: is \: \: as \: \: follows:-}}}}}[/tex]

   ★GIVEN:-

   • A Polynomial — (x^2 + x –6).

   ★TO VERIFY:-

   • Whether 2 and –3 are the roots of the Polynomial.

   ★SOLUTION:-

   [tex] \leadsto \displaystyle \sf{x^2+x-6} \\ \\ \leadsto \displaystyle \sf{x^2 + \pink{3x – 2x} – 6} \\ \\ \leadsto \displaystyle \sf{x(x + 3) – 2(x + 3)} \\ \\ \leadsto \displaystyle \sf{(x – 2)(x + 3)} \\ \\ \therefore \: \sf{x – 2 = 0 } \\ \\ \sf{ \purple{x = 2}} \: \\ \\ and \: \sf{(x + 3) = 0} \\ \\ \sf{ \purple{x = – 3}} \\ \\ \bf{so \: the \: roots \: are \: 2 \: and \: – 3}[/tex]

   First we will put 2 as the root.

   [tex] \displaystyle \sf : \longrightarrow{p(x) = x^2 + x – 6 }[/tex]

   [tex] \displaystyle \sf : \longrightarrow{p(2) = 2^2 + 2 – 6 } \\ \\ \displaystyle \sf : \longrightarrow{p(2) = 4 + 2 – 6 } \\ \\ \displaystyle \sf : \longrightarrow{p(2) = 6 – 6 } \\ \\ \displaystyle \sf : \longrightarrow{p(2) = x^2 + x – 6 } \\ \\ \therefore \:{ \boxed{ \underline{ \pink{ p(2) = 0}}}}[/tex]

   Now we will put –3 as the root.

   [tex] \displaystyle \sf : \longrightarrow{ p(-3)= (-3)^2+(-3)-6} \\ \\ \displaystyle \sf : \longrightarrow{ p(-3)= 9 – 3 – 6} \\ \\\displaystyle \sf : \longrightarrow{ p(-3)= 9 – 9} \\ \\ \therefore \: \:{ \boxed{ \underline{ \pink{ p( – 3) = 0}}}}[/tex]

   Hence, after putting 2 and –3

   The results coming is 0

   Therefore, They are the roots of the equation.

   HENCE VERIFIED

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2. Step-by-step explanation:

   Given :

   quadratic polynomial x² + x – 6

   To verify :

   2 and –3 are the zeroes of the given polynomial

   Solution :

   If ‘a’ is a zero of the polynomial p(x), then p(a) = 0

   Let p(x) = x² + x – 6

   To check if 2 is a zero of the given polynomial :

   Put x = 2,

   p(2) = 2² + 2 – 6

   = 4 + 2 – 6

   = 6 – 6

   = 0

   p(2) = 0; hence 2 is a zero of the given polynomial.

   To check if –3 is a zero of the given polynomial :

   Put x = –3,

   p(–3) = (–3)² + (–3) – 6

   = 9 – 3 – 6

   = 6 – 6

   = 0

   p(–3) = 0; hence –3 is a zero of the given polynomial.

   Hence verified!

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