Math, asked by prachikapoor63, 9 months ago

If one zero of quadric polynomial x square +(p+1)x-6 is 2,then what is the value of P?​

Answers

Answered by Intelligentcat
42

Answer:

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If one zero of quadric polynomial x square +(p+1)x-6 is 2,then what is the value of P?

\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}

Let the given polynomial be

 \sf \: p(x) =  {x}^{2}  + (p + 1)x - 6

One of the zeros of the polynomial is 2

NoTE

Sum of Zeros : - x coefficient/x² coefficient

Product of Zeros : constant term /x² coefficient

Let the other zero be a

Here,

 \tt \: 2a =  - 6 \\  \\  \longrightarrow \:   \boxed{\boxed{ \tt a =  - 3}}

The zeros of the polynomial are 2 and - 3

Also,

 \tt \:  \longrightarrow 2 + ( - 3) =  -  \dfrac{(p + 1)}{1}  \\  \\  \longrightarrow \:  \tt \:  -1 =   - (p + 1) \\  \\   \large{\longrightarrow\:  \boxed{ \boxed{ \tt \: p = 0}}}

Answered by Anonymous
11

Solution

Given :-

  • Polynomial equation, x² + (p+1)x - 6 = 0
  • First zero be 2

Find :-

  • Value of p

Explanation

We Know,

If 2 is zeros of this polynomial,

Its means that 2 is satisfied this polynomial.

So, Keep x = 2 in this polynomial,

➡ (2)² + (p+1) × 2 - 6 = 0

➡4 + 2(p+1) - 6 = 0

➡2(p + 1) = 6 - 4

➡2(p+1) = 2

➡ (p + 1) = 2/2

➡(p+1) = 1

➡p = 1 - 1

➡p = 0

Hence

  • Value of p will be 0

_________________

Answer Verification

keep value of p & x = 2 ,in given polynomial,

➡ (2)² + (0+1)×2 - 6 = 0

➡ 4 + 1 × 2 - 6 = 0

➡ 4 + 2 - 6 = 0

➡ 6 - 6 = 0

➡0 = 0

L.H.S. = R.H.S.

That's Proved.

_____________

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